In the following letter analogy, AB is related to YX through opposite positions in the alphabet. Using the same relationship, LM is related to which pair of letters?

Introduction / Context:
This analogy uses letter complements in the English alphabet. AB is mapped to YX, and you must determine how LM will be mapped using the same logic. The pattern involves pairing letters from the beginning and end of the alphabet that are equally distant from the ends, a common technique in reasoning questions involving coded letters.

Given Data / Assumptions:
- First pair: AB.
- Related pair: YX.
- Second base pair: LM.
- Options: NM, OP, IJ and GH.
- We assume that each letter of the pair is replaced individually using a positional rule, not an arbitrary whole word mapping.

Concept / Approach:
Assign positions: A is 1, B is 2, ..., Z is 26. For AB to YX, check sums: A (1) with Y (25) gives 26, and B (2) with X (24) also gives 26. So each letter is replaced by another letter such that their positions sum to 26. This is slightly different from the 27 sum pattern but follows the same complementary idea. We must now apply this 26 sum complement rule to LM.

Step-by-Step Solution:
Step 1: Confirm the relationship for AB to YX. 1 + 25 = 26 and 2 + 24 = 26, so Y and X are complements of A and B respectively. Step 2: Convert L and M to their positions. L is 12 and M is 13. Step 3: For each letter, compute 26 minus its position. For L, 26 - 12 = 14, which corresponds to N. For M, 26 - 13 = 13, which corresponds to M itself. Step 4: Therefore the complementary pair of LM under the 26 sum rule is NM. Step 5: Compare NM with the answer options and select option A.

Verification / Alternative check:
Check the sums: 12 (L) plus 14 (N) equals 26, and 13 (M) plus 13 (M) also equals 26. This mirrors the AB to YX pattern exactly. None of the other options give such consistent complement sums for both letters. For example, OP would not satisfy 26 minus position mapping for both letters starting from L and M.

Why Other Options Are Wrong:
Option B OP, option C IJ and option D GH do not result from the 26 minus position transformation on L and M. They may involve simple forward or backward shifts, but the analogy requires the same complement relationship as observed in AB to YX. Since only NM is the exact complement pair, the other options must be rejected.

Common Pitfalls:
A frequent error is to look for simple shifting patterns like moving a fixed number of positions forward or backward. Another is to miscount letter positions by one, which can produce close but incorrect answers. Carefully writing the alphabet with numbers or mentally verifying sums is essential when working with complement based analogies.

Final Answer:
Using the complement rule where positions add up to 26, LM maps to the letter pair NM.