In the following letter analogy, EF is related to JA in a particular coded way. Using the same coding pattern, which pair of letters should complete the analogy EF : JA :: NO : ?

Introduction / Context:
This analogy uses different shifts for the first and second letters of each pair. The pair EF changes to JA under a specific pattern: the first letter moves forward, while the second letter moves backward by the same number of positions. We must detect this pattern and then apply it to NO to find the correct partner pair. This type of problem checks your ability to handle more than one transformation at the same time.

Given Data / Assumptions:
First pair: EF : JA. Second pair: NO : ?. All letters are capital letters from A to Z. The relationship for the first and second letters in a pair may differ but must be consistent across both pairs.

Concept / Approach:
The first step is to write the alphabet positions for E, F, J, and A. By examining the differences, we may find that the first letter of the pair moves forward by a fixed number of positions and the second letter moves backward by the same number of positions. Once we identify that number as 5, we can apply +5 to the first letter of NO and -5 to the second letter to derive the missing pair. This dual shift pattern is common in coding and analogy questions.

Step-by-Step Solution:
Step 1: Compute positions for EF and JA. E = 5, F = 6. J = 10, A = 1. Step 2: Analyse the shift for the first letter. From E (5) to J (10) is an increase of +5. So the first letter of the coded pair is obtained by adding 5. Step 3: Analyse the shift for the second letter. From F (6) to A (1) is a decrease of 5, that is 6 - 5 = 1. So the second letter of the coded pair is obtained by subtracting 5. Step 4: Apply the same pattern to NO. N is 14. Add 5 to get 19, which is S. O is 15. Subtract 5 to get 10, which is J. Therefore, NO becomes SJ.

Verification / Alternative check:
We can rewrite the rule as: first coded letter = original first letter + 5, second coded letter = original second letter - 5. For EF, that gives J and A, which matches JA. For NO, that gives S and J, which matches SJ. If we tried any other pattern, such as adding the same value to both letters, we would not reproduce JA from EF. The dual shift pattern is therefore confirmed to be the correct coding rule.

Why Other Options Are Wrong:
TI, RK, and HU cannot be obtained by applying +5 to N and -5 to O simultaneously. PL uses a backward shift for the first letter and a different shift for the second, which does not match the pattern from EF to JA.

Common Pitfalls:
A typical mistake is to assume the same shift applies to both letters in a pair and then become confused when that does not map EF to JA. Another pitfall is to only check the transformation for the first letter and ignore the second, which can lead to wrong conclusions about the rule. Always examine both letters and be open to patterns where the first and second letters are treated differently but in a consistent and symmetrical manner.

Final Answer:
Using the same +5 and -5 pattern, NO is encoded as SJ.