In this letter pair analogy, “JPC is to GMZ as PUV is to ______”. Select the group of letters that completes the analogy by following the same backward alphabet shift pattern.

Introduction / Context:
This analogy uses a fixed backward shift in the alphabet to transform one group of letters into another. The pair “JPC : GMZ” shows how each letter of JPC is mapped to the corresponding letter in GMZ by subtracting a constant number of positions. We must discover that constant shift and then apply it to PUV to determine which option correctly completes the analogy. Such questions assess accuracy in working with alphabet positions and modular arithmetic on letters.

Given Data / Assumptions:

• Example pair: JPC → GMZ. • Target pair: PUV → ? • Options: MRS, MSR, MQR, RMS. • Alphabet positions: A = 1, B = 2, ..., Z = 26 with wrapping when shifting backward past A.

Concept / Approach:
We determine the shift by converting each letter in the example pair into its numeric position and subtracting. If we see the same difference for all positions, that difference is the constant shift. Then we apply the same subtraction to each letter in PUV. Finally, we match the resulting letter group with one of the provided options, paying attention to both letters and their order.

Step-by-Step Solution:
Step 1: Convert JPC and GMZ to numeric positions. J = 10, P = 16, C = 3. G = 7, M = 13, Z = 26. Step 2: Find the shifts from JPC to GMZ. 10 → 7: −3. 16 → 13: −3. 3 → 26: this is effectively 3 − 3 = 0, wrap to 26 (Z), which is also −3 modulo 26. So the transformation is “subtract 3 from each position, wrapping around if needed”. Step 3: Apply the same rule to PUV. P = 16, U = 21, V = 22. 16 − 3 = 13 → M. 21 − 3 = 18 → R. 22 − 3 = 19 → S. Step 4: The resulting group is M R S (MRS).

Verification / Alternative check:
We can confirm the consistency by applying the reverse shift (adding 3) to GMZ and MRS. G (7) + 3 = J (10), M (13) + 3 = P (16), Z (26) + 3 = 29, minus 26 = 3 → C, returning JPC. Similarly, M (13) + 3 = P (16), R (18) + 3 = U (21), S (19) + 3 = V (22), returning PUV. This confirms that a uniform −3 shift generates both GMZ from JPC and MRS from PUV.

Why Other Options Are Wrong:
• MSR and RMS: These options use the same letters M, R, and S but in different orders, which breaks the position wise mapping produced by the precise −3 shift rule. • MQR: Contains incorrect letters that do not arise from subtracting 3 from P, U, and V respectively.

Common Pitfalls:
A common error is to observe only the letters present in the options and pick one that looks similar without checking the shift for each position. Another pitfall is forgetting the wrap around from A to Z when subtracting. Handling modular arithmetic on letters carefully and verifying the mapping in both directions prevents such mistakes.

Final Answer:
The group of letters that correctly completes the analogy is MRS.