A series of letter pairs is given with one term missing. Select the correct alternative from the given options that will complete the series PR, VX, BD, ?

Introduction / Context:
This question presents a sequence of two letter combinations where both letters in each pair change according to an alphabetical rule. The student must recognise the positional relationship between corresponding letters of consecutive pairs and then extend the pattern to find the missing pair. This type of alphabet test problem develops the ability to handle cyclic and modular changes in letter positions.

Given Data / Assumptions:

• The given series is PR, VX, BD, ?
• Each item consists of exactly two uppercase letters.
• We assume standard alphabetical positions A = 1 to Z = 26.
• The same transformation pattern is expected to continue throughout the series.

Concept / Approach:
We separate the sequence into one series of first letters and another of second letters, and then examine how each sub series progresses. The pattern might involve adding a fixed number modulo 26, or jumping across the alphabet in a cyclic manner. It is important to treat the alphabet as cyclic so that when we go beyond Z, we come back to A.

Step-by-Step Solution:
Step 1: Consider the first letters: P, V, B. Their positions are P = 16, V = 22, B = 2. Step 2: From P (16) to V (22) the difference is plus 6. From V (22) to B (2) the difference is also plus 6 if we move cyclically, because 22 plus 6 equals 28 and 28 minus 26 equals 2. Step 3: Applying the same plus 6 pattern again, from B (2) we add 6 to get 8, which corresponds to H. So the first letter of the missing pair must be H. Step 4: Now consider the second letters: R, X, D. Their positions are R = 18, X = 24, D = 4. Step 5: From R (18) to X (24) the difference is plus 6. From X (24) to D (4) is also plus 6 in a cyclic sense because 24 plus 6 equals 30 and 30 minus 26 equals 4. Step 6: Apply the same rule again: from D (4) add 6 to get 10, which corresponds to J. Step 7: Hence, the missing pair is HJ.

Verification / Alternative check:
We can quickly verify that every step in the sequence obeys the rule letter position new equals letter position old plus 6, computed modulo 26, independently for both letters. Each given pair and the derived pair HJ satisfies this rule perfectly. No other option yields such regular cyclic increments for both letters.

Why Other Options Are Wrong:
EF, HI, and HK do not all satisfy a consistent plus 6 progression from BD when checked numerically. For example, HI would require the first letter to be H (correct) but the second letter I corresponds to position 9, which is not equal to D (4) plus 6 modulo 26. HK similarly fails for the second letter. Therefore, these options break the established pattern and are incorrect. The none of these option is not valid because HJ clearly follows the required rule.

Common Pitfalls:
Students may treat the alphabet as non cyclic and become confused when the sequence crosses from Z back to A. Others may focus only on the pattern of first letters and then guess the second letter based on intuition. A disciplined approach that uses modular arithmetic for both letters prevents these issues.

Final Answer:
The pair of letters that correctly completes the series is HJ.