In the pair of codes "HFZ : LJD :: KTM : ____", which option applies the same +4 letter shift?

Introduction / Context:
This analogy deals with a fixed forward shift in the alphabet between a word and its coded form. In the pair "HFZ : LJD", each letter of HFZ is converted to the corresponding letter in LJD by moving forward in the alphabet by the same amount, wrapping around from Z to A if required. The task is to find, among the options, a pair that shows exactly the same type of transformation.

Given Data / Assumptions:

• Model pair: HFZ coded as LJD.
• Options each contain a small pair of three letter groups.
• Alphabet positions: A = 1, B = 2, ..., Z = 26.
• The shift should be constant for all three letters within a pair.

Concept / Approach:
Find the shift in the model pair first. H is the 8th letter and L is the 12th. F is the 6th letter and J is the 10th. Z is the 26th letter and D is the 4th. Going from 8 to 12 is a change of plus 4. From 6 to 10 is also plus 4. When we add 4 to 26 (Z), we exceed 26, so we wrap around: 26 + 4 = 30, and 30 - 26 = 4, which is D. Thus the rule is: add 4 to each letter position, wrapping around after Z. Now we must find which option pair shows the same pattern.

Step-by-Step Solution:

Verify the model pair: H → L, F → J, Z → D, each with a +4 shift. Check option KTM : OXQ. K = 11, T = 20, M = 13. Add 4: 11 + 4 = 15 (O), 20 + 4 = 24 (X), 13 + 4 = 17 (Q). Observe that KTM becomes OXQ under a +4 shift. Confirm that other options do not show a uniform +4 shift for all letters.

Verification / Alternative check:
For KBN : LCO, K = 11 becomes L = 12 (+1), but B = 2 becomes C = 3 (+1), and N = 14 becomes O = 15 (+1). This is a +1 shift, not +4. For BHO : DJQ, B = 2 to D = 4 is +2, H = 8 to J = 10 is +2, and O = 15 to Q = 17 is +2, so this pair uses +2. FKU : INX has F = 6 to I = 9, which is +3, and so on. None of them use the consistent +4 shift that HFZ : LJD uses. Only KTM : OXQ matches the pattern exactly.

Why Other Options Are Wrong:
Each incorrect option uses a different constant shift or a mix of shifts that do not equal +4 for all letters. Since the model clearly applies +4 uniformly, any deviation from this transformation breaks the analogy. The question requires the same type and magnitude of shift, so all non matching pairs must be discarded.

Common Pitfalls:
Test takers sometimes only compare the first letter of each pair and assume the same shift holds for the rest without verification. Others confuse wrapping around the alphabet, especially when dealing with letters near the end like Z. The safest approach is to calculate the difference for each letter carefully and check consistency.

Final Answer:
The pair that follows the same +4 letter shift rule as HFZ : LJD is KTM : OXQ.