In the pair series RS, ZA, HI, which of the following letter pairs should come next to continue the pattern correctly?

Introduction / Context:
This pair series tests your ability to identify hidden arithmetic patterns in the positions of letters. Each term consists of two letters and the same transformation rule applies from one pair to the next. Questions of this sort often require careful handling of modular arithmetic in the alphabet because the sequence can wrap around from Z back to A. Understanding this helps you deal with many alphabet reasoning problems in exams.

Given Data / Assumptions:
- Given series: RS, ZA, HI, ? - Each term has exactly two capital letters. - A uniform pattern is assumed for both letters of each pair. span style="display:block;">- Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
We treat the first letters of all pairs as one sequence and the second letters as another. For each sequence, we compute numerical positions and check for a consistent step size. Because Z is at the end of the alphabet, the jump from S to Z and from Z to H might involve wrap around arithmetic. Once we see the pattern in how positions change, we extend it by one step to find the next pair. Careful attention to the magnitude and direction of the step is essential.

Step-by-Step Solution:
Step 1: Convert each pair to positions. RS: R (18), S (19). ZA: Z (26), A (1). HI: H (8), I (9). Step 2: Study the first letter sequence: R, Z, H. Positions: 18, 26, 8. From R (18) to Z (26): difference is +8. From Z (26) to H (8): working in mod 26, 26 + 8 = 34, and 34 - 26 = 8, so difference is effectively +8 again. So the first letter moves +8 each time in a circular alphabet. Next step: 8 + 8 = 16, corresponding to P. Step 3: Study the second letter sequence: S, A, I. Positions: 19, 1, 9. From S (19) to A (1): using wrap around, 19 + 8 = 27, and 27 - 26 = 1, so a jump of +8. From A (1) to I (9): again +8. The second letter also moves +8 each time. Next: 9 + 8 = 17, which is Q. Step 4: Combine the predicted letters. First letter P and second letter Q give the pair PQ.

Verification / Alternative check:
We can summarise the numeric pattern clearly: First letters: 18, 26, 8, 16 (each adding 8 mod 26). Second letters: 19, 1, 9, 17 (each adding 8 mod 26). The consistency of these increments confirms that the rule is a simple +8 shift for both letters with wrap around. The pair PQ precisely fits this rule. Any other candidate pair would break the +8 movement for at least one of the positions, so PQ is uniquely correct.

Why Other Options Are Wrong:
A) LM corresponds to positions 12 and 13, which do not result from adding 8 to H (8) and I (9). B) KL gives 11 and 12, again violating the +8 increment pattern. D) PR has R (18) as the second letter, whereas the rule requires Q (17) after I, not R.

Common Pitfalls:
One major pitfall is failing to consider wrap around arithmetic when crossing from Z back to A. Some candidates treat Z as a hard end and do not apply circular reasoning, which hides the constant step pattern. Another error is to rely on rough visual distance between letters without checking actual positions. The best approach is always to convert letters to numbers and compute differences formally, especially in series that include Z or A near the edges of the alphabet.

Final Answer:
The letter pair that correctly completes the series RS, ZA, HI, ? is PQ.