A series of letter pairs is given with one pair missing. Select the pair that follows the same pattern: RS, ?, BC, GH.

Introduction / Context:
This alphabet series uses letter pairs that move around the alphabet in equal steps. Your task is to identify the missing pair that keeps the transformation consistent from RS through to BC and GH. Such questions often require modular arithmetic because the sequence wraps from Z back to A.

Given Data / Assumptions:

• Known pairs: RS, ?, BC, GH. • We consider A = 1, ..., Z = 26 and apply additions modulo 26. • The same numeric shift is used to move from one pair to the next. • The rule is applied independently to the first and second letters but with equal step sizes.

Concept / Approach:
We hypothesize that there is a constant step between consecutive pairs when viewed modulo 26. Thus, starting from RS we add a fixed number to get the next pair, and from that pair we add the same number again to obtain BC, and so on. Because the alphabet cycles, addition beyond Z wraps around to the beginning. We must determine this step size.

Step-by-Step Solution:
Step 1: Convert letters to positions. R = 18, S = 19, B = 2, C = 3, G = 7, H = 8. Step 2: Determine the step from the missing pair to BC and from BC to GH. From B (2) to G (7) we add 5. From C (3) to H (8) we also add 5. So the transition from BC to GH is +5 for both letters. Step 3: Assume the same +5 step holds from RS to the missing pair and from the missing pair to BC. Apply +5 to R and S: 18 + 5 = 23 (W), 19 + 5 = 24 (X). So the pair after RS should be WX. Step 4: Verify that applying +5 again yields BC. W is 23, 23 + 5 = 28, 28 − 26 = 2 (B). X is 24, 24 + 5 = 29, 29 − 26 = 3 (C). This matches BC.

Verification / Alternative check:
We now have a sequence of pairs: RS, WX, BC, GH. Each transformation adds 5 to the letters modulo 26. This pattern holds for both letters in every step. None of the other options, if placed as the missing pair, would allow this consistent +5 progression to produce BC and GH correctly.

Why Other Options Are Wrong:
• XY: If we use XY, then from XY to BC the step would not be +5 modulo 26 for both letters. • UV: Inserting UV breaks the uniform step pattern and fails to map neatly to BC and GH using a single constant step. • GE: This pair does not fit any single step pattern linking RS, GE, BC, and GH, and specifically conflicts with the observed +5 from BC to GH.

Common Pitfalls:
Exam takers sometimes forget to use modulo arithmetic when letters pass beyond Z. Others may only check the step between RS and the missing pair and ignore the later steps, causing inconsistent choices. It is essential to verify that one constant step size works for the entire sequence.

Final Answer:
The missing pair that correctly continues the pattern is WX.