In this letter analogy, “AF is to BE as ______ is to DH”. Select the pair of letters that completes the analogy by following the same pattern of increasing the first letter and decreasing the second letter.

Introduction / Context:
This analogy involves pairs of letters where each letter in the pair changes in a specific way to produce the corresponding pair. The example AF : BE shows that the transformation is not simply a uniform shift, but a combination of increasing one letter and decreasing the other. The task is to determine how AF becomes BE and then find the letter pair that will similarly become DH. Such problems check your comfort with alphabet positions and two step transformations.

Given Data / Assumptions:

• Example pair: AF maps to BE. • Target mapping: ? maps to DH. • Options: CH, CG, DG, CI. • Alphabet positions are taken as A = 1, B = 2, ..., Z = 26.

Concept / Approach:
We treat each pair as two separate letters. For AF → BE, we analyse first letters (A and B) and second letters (F and E) separately. The first letters may be shifted forward, while the second letters may be shifted backward. Once we know exactly how many steps each letter is moved, we can set up equations to find which starting pair would transform into DH with the same rule.

Step-by-Step Solution:
Step 1: Convert AF and BE to positions. A = 1, F = 6. B = 2, E = 5. Step 2: Check the first letters. A (1) becomes B (2), so the first letter is shifted +1. Step 3: Check the second letters. F (6) becomes E (5), so the second letter is shifted −1. Step 4: Express the rule. First letter: position + 1. Second letter: position − 1. Step 5: Apply this rule in reverse to DH. Let the unknown pair be XY such that XY → DH under the same rule. For the first position: X + 1 = D (4), so X = 3 → C. For the second position: Y − 1 = H (8), so Y = 9 → I. Thus, the starting pair must be CI.

Verification / Alternative check:
Verify by applying the discovered rule directly to CI. For the first letter, C (3) + 1 = D (4). For the second letter, I (9) − 1 = H (8). So CI indeed maps to DH, and AF maps to BE under the same transformation scheme. No other option produces DH when this rule is applied, which confirms that CI is the only correct answer.

Why Other Options Are Wrong:
• CH: Applying the rule gives DH for the first letter but G for the second letter, so the result is DG, not DH. • CG: Here the first letter would still become D, but the second would become F, giving DF rather than DH. • DG: This pair already contains D as the first letter; shifting it would not produce DH under the same rule.

Common Pitfalls:
One common error is to look for a constant shift in both letters, such as adding the same number to each position. However, AF to BE clearly does not use a uniform shift. Another pitfall is to test options by guesswork rather than reconstructing the original pair through algebraic reasoning. Working backward from the known result DH using the precise rule helps avoid confusion and ensures accuracy.

Final Answer:
The pair of letters that correctly completes the analogy is CI.