In the triplet series PRQ, UWV, ZBA, ?, JLK, which triplet should replace the question mark to continue the pattern?

Introduction / Context:
The series PRQ, UWV, ZBA, ?, JLK is a three letter alphabet sequence. Each triplet follows a specific internal pattern, and the triplets as a whole follow another pattern. To find the missing term, we need to examine both the evolution inside each triplet and the evolution across triplets.

Given Data / Assumptions:

• Triplets: PRQ, UWV, ZBA, ?, JLK.
• Alphabet positions A 1 to Z 26.
• Each triplet has three letters that appear to change by a small fixed step within the triplet.

Concept / Approach:
We first analyse how letters move inside each triplet. Then we look at how the first letters of each triplet change across the series, and then the second and third letters across triplets. This two layer pattern is common in higher difficulty alphabet series problems, but the arithmetic behind it is straightforward.

Step-by-Step Solution:
Step 1: Consider PRQ. Positions: P 16, R 18, Q 17. Differences inside the triplet are plus 2 then minus 1. Step 2: Consider UWV. Positions: U 21, W 23, V 22, again plus 2 then minus 1. Step 3: Consider ZBA. Positions: Z 26, B 2, A 1. If we work modulo 26, then from 26 to 2 is plus 2 (26 plus 2 equals 28, minus 26 equals 2), and from 2 to 1 is minus 1. Step 4: Consider JLK. Positions: J 10, L 12, K 11, again plus 2 then minus 1. Step 5: So each triplet has the internal pattern first letter, first plus 2, that result minus 1. Step 6: Now look at the first letters of the triplets: P, U, Z, ?, J. Step 7: Positions: P 16, U 21, Z 26, J 10. Step 8: Differences from P to U to Z are plus 5 and plus 5. From Z to the unknown first letter and then to J should also follow plus 5 steps modulo 26. Step 9: Starting at 26 Z, add 5: 26 plus 5 equals 31, minus 26 equals 5, which is E. Then add 5 again: 5 plus 5 equals 10, which is J, matching the last triplet. Step 10: So the missing first letter is E. Step 11: Use the internal rule plus 2 then minus 1. From E 5, plus 2 gives 7 G. Then 7 minus 1 gives 6 F. Step 12: Therefore the missing triplet is EGF.

Verification / Alternative check:
Write all triplets including EGF in numeric form: PRQ 16,18,17; UWV 21,23,22; ZBA 26,2,1; EGF 5,7,6; JLK 10,12,11. Every triplet internally has the pattern plus 2 then minus 1. First letters are 16, 21, 26, 5, 10, an arithmetic progression with step plus 5 modulo 26. The same is true for the second and third letters when you apply the internal rule. This confirms EGF fits perfectly.

Why Other Options Are Wrong:
FHG, DFE, FGE, and EHF do not have the internal structure plus 2 then minus 1 starting from a first letter that still fits the plus 5 progression of first letters. For example, starting with F would give the next first letter as K, not J. Only EGF maintains both the inter triplet and intra triplet patterns.

Common Pitfalls:
One pitfall is to focus only on internal differences inside each triplet and ignore the pattern across triplets. Another is to treat letter movements as random jumps instead of tracking them systematically with modular arithmetic. A clear, column wise numeric approach helps avoid these mistakes.

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