In the triplet series UPM, BWT, IDA, PKH, ?, which of the following triplets should come next to continue the pattern?

Introduction / Context:
This question gives a series of three letter groups: UPM, BWT, IDA, PKH, ?, and asks for the next triplet. It is a typical alphabet series where each position of the triplet follows its own arithmetic progression in the alphabet with a fixed step and wrap around from Z to A.

Given Data / Assumptions:

• Triplets: UPM, BWT, IDA, PKH, ?
• First letter sequence: U, B, I, P, ?
• Second letter sequence: P, W, D, K, ?
• Third letter sequence: M, T, A, H, ?
• Alphabet positions A 1 to Z 26.

Concept / Approach:
The strategy is to study each column separately. In many such questions, corresponding letters across triplets are generated by adding a constant number modulo 26. Once the step size is identified for each column, we apply it again to find the next letters in that column. Finally, we join those three letters to form the missing triplet.

Step-by-Step Solution:
Step 1: Convert the first letters U, B, I, P to positions: U 21, B 2, I 9, P 16. Step 2: Compute differences moving forward modulo 26: From 21 to 2 is +7 (21 + 7 equals 28, minus 26 is 2). From 2 to 9 is +7, and from 9 to 16 is +7. Step 3: Continue the pattern: 16 + 7 equals 23, which is W. So the next first letter is W. Step 4: Convert second letters P, W, D, K to numbers: P 16, W 23, D 4, K 11. Step 5: Check differences: 16 to 23 is +7, 23 to 4 is +7 modulo 26 (23 + 7 equals 30, minus 26 is 4), and 4 to 11 is +7. Step 6: Continue: 11 + 7 equals 18, which corresponds to R. So the next second letter is R. Step 7: Convert third letters M, T, A, H to numbers: M 13, T 20, A 1, H 8. Step 8: Differences: 13 to 20 is +7, 20 to 1 is +7 modulo 26, and 1 to 8 is +7. Step 9: Continue: 8 + 7 equals 15, which corresponds to O. So the next third letter is O. Step 10: Putting all three results together, the missing triplet is WRO.

Verification / Alternative check:
Write the numeric forms of the extended sequence: UPM (21,16,13), BWT (2,23,20), IDA (9,4,1), PKH (16,11,8), WRO (23,18,15). Every column increases by 7 modulo 26: 21,2,9,16,23; 16,23,4,11,18; 13,20,1,8,15. This confirms a perfect uniform pattern, and WRO fits it exactly.

Why Other Options Are Wrong:
WPR has the correct first letter W but second letter P 16 and third letter R 18, which break the plus 7 step in the second and third columns. XPO starts with X 24 instead of W 23, ignoring the established increment. XRS and VQL also fail to maintain the +7 progression in all of the three sequences.

Common Pitfalls:
Some candidates look for a pattern only among the first letters and then guess a triplet that seems visually similar. Others overlook the wrap around behaviour from Z to A, which is crucial when seeing transitions like U to B or W to D. You should always check each column separately and verify that your candidate maintains the same numeric difference, including wrap around, for all positions.

Final Answer:
The triplet that correctly continues the series is WRO.