Pair analogy on intra-pair gap: 'CG : EI :: FJ : ____' — identify the invariant letter-gap property within each pair and select the option that preserves the same structural relation.

Introduction / Context:
In pair analogies, a robust tactic is to look for a property that both letters in each pair share, such as the fixed distance between the first and second letters. For “CG : EI,” notice that in each pair the second letter is a fixed number of positions ahead of the first. The task is to identify that intra-pair gap and then pick the option whose letters obey the same gap for “FJ : ____”.

Given Data / Assumptions:

• Positions: A=1 to Z=26.
• C→G: 3→7, gap +4.
• E→I: 5→9, gap +4.
• Therefore, each pair shows “second letter = first letter + 4”.
• We must select the choice where the second letter is also +4 from the first.

Concept / Approach:
Compute gaps in the options: LM has M − L = +1; IJ has J − I = +1; GK has K − G = +4; JK has K − J = +1. Only “GK” matches the required +4 difference. Note that another plausible interpretation of CG→EI is a pairwise +2 shift applied left-to-right; however, applying +2 to FJ would yield HL, which is not among the options. Hence, the invariant intra-pair distance property is the intended discriminator.

Step-by-Step Solution:
1) Establish the invariant: in both CG and EI, the second letter is four positions ahead of the first.2) Check each option's gap.3) Identify GK as the only pair with a +4 gap.4) Conclude FJ : GK preserves the same structural relation.

Verification / Alternative check:
Recompute numerically: G(7)→K(11) difference is +4, consistent with C→G and E→I. No other option maintains this exact intra-pair spacing.

Why Other Options Are Wrong:
LM, IJ, and JK all have only a +1 gap, breaking the structural rule identified in the base pairs.

Common Pitfalls:
Committing to a letter-wise +2 mapping and ignoring the answer set, which points strongly to gap preservation as the governing constraint.

Final Answer:
GK