Analogy of letter-wise shifts: 'ABA : ECE :: ____ : ____' — detect and apply the per-position shift pattern (+4 to 1st and 3rd letters; +1 to the middle letter) to find the correctly mapped pair.

Introduction / Context:
Letter analogies often encode a fixed shift applied position by position. In the pair “ABA : ECE”, the left and right members follow a precise mapping at each character index. To solve “ABA : ECE :: ____ : ____”, we must identify that mapping and then apply it to the left member of each option to see which yields the stated right member perfectly.

Given Data / Assumptions:

• Alphabet positions: A=1, B=2, C=3, ..., Z=26.
• Given source: A B A → target: E C E.
• Mapping is applied independently to index 1, 2, and 3.

Concept / Approach:
Compute shifts: A→E is +4, B→C is +1, and A→E is again +4. Thus the per-position rule is: index1 +4, index2 +1, index3 +4 (with wraparound if needed). We test each option's left triplet by applying this rule and check whether we obtain its right triplet exactly.

Step-by-Step Solution:
1) Rule extraction from ABA→ECE: (+4, +1, +4).2) Test A: L M L → apply → (P, N, P) but given right is N O N, mismatch.3) Test B: I D I → apply → (M, E, M) but given right is O F O, mismatch.4) Test C: P Q P → apply → (T, R, T) but given right is S T S, mismatch.5) Test D: C D C → apply → (G, E, G) which matches G E G exactly.

Verification / Alternative check:
Reversing the rule on GEG should return CDC: G→C is −4, E→D is −1, G→C is −4. This perfect reversibility confirms the mapping is coherent and uniquely satisfied by option D.

Why Other Options Are Wrong:
Each fails at least one index when the precise (+4, +1, +4) rule is applied, producing mismatched letters versus the option's stated right-hand side.

Common Pitfalls:
Applying a uniform shift to all three positions or comparing only the first characters. This puzzle demands index-specific shifts.

Final Answer:
CDC : GEG