Choose the correct alternative that will replace the question mark in the series DHL, PTX, BFJ, ?

Introduction / Context:
Here you are given a series of three letter groups: DHL, PTX, BFJ, ?. The task is to find the next three letter group that fits the hidden pattern. This is a classic alphabet coding problem where letters move in steps around the alphabet. What makes this series interesting is that all three positions in each triplet follow the same positional rule, but from different starting points.

Given Data / Assumptions:

• Known terms: DHL, PTX, BFJ.
• Each triplet has three letters, which we can treat as first, second, and third positions in separate sequences.
• Alphabet positions are A 1 to Z 26, and after Z we can wrap around to A when adding a fixed amount.
• The same constant difference appears repeatedly in each sequence when considered modulo 26.

Concept / Approach:
The cleanest way is to treat each of the three positions separately. For the first letters we consider D, P, and B as a sequence. For the second letters we consider H, T, and F, and for the third letters L, X, and J. If each of these follows a regular arithmetic progression in the alphabet, then the next term in each progression gives us the three letters of the missing triplet.

Step-by-Step Solution:
Step 1: Convert the first letters to numbers: D 4, P 16, B 2. Step 2: Notice that 4 to 16 is an increase of 12, and 16 to 2 is also effectively an increase of 12 if we work modulo 26 (16 + 12 = 28, and 28 minus 26 equals 2). Step 3: Continue this pattern: 2 + 12 equals 14, which corresponds to N. So the first letter of the missing triplet is N. Step 4: Now convert the second letters: H 8, T 20, F 6. Again, 8 to 20 is +12, and 20 to 6 is +12 modulo 26. Step 5: Add 12 to 6: 6 + 12 equals 18, corresponding to R. So the second letter is R. Step 6: For the third letters: L 12, X 24, J 10. We see 12 to 24 is +12, and 24 to 10 is also +12 modulo 26. Step 7: Add 12 to 10 to get 22, which is V. So the third letter is V, and the missing triplet is NRV.

Verification / Alternative check:
Write out all four triplets with their numeric positions: DHL (4,8,12), PTX (16,20,24), BFJ (2,6,10), NRV (14,18,22). For each column we have 4,16,2,14; 8,20,6,18; 12,24,10,22, each time adding 12 modulo 26. This confirms a uniform rule for all three positions. No other listed option creates such a consistent three column pattern with a constant step of 12.

Why Other Options Are Wrong:
Options like KOS, NPS, or NRU break the strict plus 12 pattern in at least one of the letter positions. For example, KOS would give first letter K 11 instead of 14, and the progression 4,16,2,11 does not have a constant difference. Similarly, NRU changes the last letter from the required V 22 to U 21, again breaking the consistent arithmetic progression in the third column.

Common Pitfalls:
A common mistake is to look only at the first letters and stop once a partial pattern is found, without checking the second and third letters. Another pitfall is forgetting to use modulo 26 arithmetic and concluding that the numbers do not follow a regular step, when in fact they do after wrapping around the alphabet. Always compute the differences carefully and apply the same logic to all three positions.

Final Answer:
The correct triplet that replaces the question mark is NRV.