In the alphabet series DEC, HIG, LMK, PQO, TUS, which of the following three-letter groups should appear next to maintain the pattern?

Introduction / Context:
This alphabet-series problem presents triplets such as DEC, HIG and TUS. Each group appears to follow a small internal pattern involving movement forward and backward in the alphabet. The goal is to extend this pattern logically to find the next triplet. Such questions train students to map letters into numeric positions and observe repeated operations in a consistent way.

Given Data / Assumptions:

• Provided series: DEC, HIG, LMK, PQO, TUS, ?.• Each triplet has the pattern first letter, next letter, and then a letter two steps back.• The starting letters are D, H, L, P, T, and we must find the next starting letter.• The internal pattern of +1 and −2 appears within each triplet.

Concept / Approach:
First, we examine the structure of each triplet. For DEC, the letters are D, E, C, which correspond to +1 and then −2 relative to the first letter. HIG gives H, I, G with the same pattern. The same structure holds for LMK and PQO, and for TUS. Then we study the sequence of the starting letters themselves to see how they move along the alphabet. Once both the internal pattern and the starting letter progression are identified, the next triplet is determined uniquely.

Step-by-Step Solution:
Consider the start letters: D, H, L, P, T.Numeric positions: D=4, H=8, L=12, P=16, T=20.The differences are +4 each time (8−4, 12−8, 16−12, 20−16).Therefore, the next starting letter = 20 + 4 = 24, which is X.Internal structure: For DEC, starting from D, the sequence is D, E (D+1), C (D−1 or E−2). For HIG, it is H, I, G; for LMK, L, M, K; for PQO, P, Q, O; for TUS, T, U, S.Thus the pattern inside each triplet is first letter, first letter + 1, first letter − 1.Using X as the start, we get X, Y, W as the next triplet.

Verification / Alternative check:
We can verify by reconstructing each term numerically. For example, LMK uses 12, 13, 11 and PQO uses 16, 17, 15, which clearly show +1 and −1 relative to the first letter. Applying the same logic to X yields 24, 25, 23 which map to X, Y, W. Among the options, only XYW matches this structure exactly.

Why Other Options Are Wrong:
XYZ is purely ascending and does not include the required backward step. WXY starts at W, not X, and breaks the +4 pattern for starting letters. YZA begins with Y and also fails both the starting-letter pattern and the internal +1, −1 structure. Therefore, these alternatives cannot be accepted as valid continuations of the given series.

Common Pitfalls:
One common mistake is to treat the triplets as simple ascending blocks and ignore the backward movement of the third letter. Another pitfall is focusing only on the internal structure without noticing that the starting letters themselves move in regular steps of four. Accurate solutions require checking both aspects of the pattern.

Final Answer:
XYW