In this letter analogy, DGI is related to JMO. Using the same pattern, which group of letters should complete the analogy DGI : JMO :: RUW : ?

Introduction / Context:
This question tests the ability to detect consistent numerical shifts in alphabet positions for groups of letters. The analogy DGI : JMO suggests a specific transformation applied to each letter. Once this rule is found, it must be applied to RUW to find the missing group. Such problems require careful counting and attention to the pattern used across all positions.

Given Data / Assumptions:
First pair: DGI : JMO. Second pair: RUW : ?. All letters are English capital letters. The same transformation is applied to each corresponding letter.

Concept / Approach:
We convert each letter to its alphabet position and compare the first and second groups position wise. If the differences are consistent, that difference becomes the rule for the analogy. The same difference is then applied to the letters in RUW. Because we might cross beyond Z, thinking about wrapping around the alphabet is also important in these problems.

Step-by-Step Solution:
Step 1: Convert DGI to positions. D = 4, G = 7, I = 9. Step 2: Convert JMO to positions. J = 10, M = 13, O = 15. Step 3: Find the difference for each letter. 4 to 10 is +6. 7 to 13 is +6. 9 to 15 is +6. So every letter in DGI is shifted six positions forward to get JMO. Step 4: Apply the same +6 rule to RUW. R = 18, U = 21, W = 23. 18 + 6 = 24, which is X. 21 + 6 = 27. Alphabet positions go from 1 to 26, so 27 wraps to 1, which is A. 23 + 6 = 29. Subtract 26 to wrap around, 29 - 26 = 3, which is C. Thus RUW becomes XAC.

Verification / Alternative check:
To verify, shift XAC six positions backward. X (24) minus 6 is 18, which is R. A (1) minus 6 would give -5, and wrapping forward by adding 26 gives 21, which is U. C (3) minus 6 gives -3, and -3 plus 26 is 23, which is W. This reverse operation returns RUW exactly, confirming that XAC is consistent with the original pattern between DGI and JMO.

Why Other Options Are Wrong:
WYZ does not result from adding 6 to each letter in RUW and also breaks the wrap around logic. ACE is unrelated to RUW under any constant shift of +6 and is simply a basic sequence. ZAC approximates some wrap around behaviour but does not match the precise +6 pattern from DGI to JMO. VBD also fails to follow the uniform +6 shift from R, U, and W.

Common Pitfalls:
When letters are near the end of the alphabet, many learners forget to wrap around after Z and instead stop counting or miscalculate. It is essential to treat the alphabet cyclically when large positive shifts are involved. Another mistake is to assume different shifts for each letter. In classical analogy questions of this type, the safest assumption is a single consistent rule for all positions unless clearly indicated otherwise.

Final Answer:
The correct group of letters that completes the analogy is XAC.