In the letter pairs HP, CJ, FN and RZ, identify the odd pair based on the fixed alphabetical gap between the letters.

Introduction / Context:
This question belongs to the alphabet coding and reasoning category. Each option is a pair of letters, and the task is to find which pair does not follow the same pattern in terms of alphabetic positions. Specifically, we look at the fixed gap between the two letters in each pair. Such questions are common in reasoning sections of competitive exams and help train the ability to map letters to numbers and observe regular steps.

Given Data / Assumptions:
The given letter pairs are HP, CJ, FN and RZ. We use the usual alphabet positions: A = 1, B = 2, C = 3, up to Z = 26. We compute the difference in position between the second letter and the first letter in each pair. We are looking for a common gap value that three pairs share, while one pair has a different gap.

Concept / Approach:
The strategy is to convert letters into numbers, then subtract the position of the first letter from the position of the second letter. If three pairs show the same difference, such as plus 8, and the fourth pair shows a different difference, then the fourth pair is the odd one out. This numerical viewpoint simplifies what can otherwise look like arbitrary letter pairs.

Step-by-Step Solution:
Step 1: For HP, H is the 8th letter and P is the 16th letter of the alphabet. The difference is 16 - 8 = 8. Step 2: For FN, F is the 6th letter and N is the 14th letter. The difference is 14 - 6 = 8. Step 3: For RZ, R is the 18th letter and Z is the 26th letter. The difference is 26 - 18 = 8. Step 4: For CJ, C is the 3rd letter and J is the 10th letter. The difference is 10 - 3 = 7. Step 5: We observe that HP, FN and RZ all have a gap of 8 positions between their letters, while CJ has a gap of 7 positions. Step 6: Therefore, CJ does not follow the same fixed gap rule and is the odd pair in this set.

Verification / Alternative check:
Write the alphabet and count manually from the first letter to the second in each pair to confirm the gaps. In HP, FN and RZ, there are seven letters in between, making a movement of eight positions, while between C and J there are only six letters in between, corresponding to a movement of seven positions. Since the difference for CJ cannot be adjusted to match the consistent gap of 8 seen in the other three pairs, the classification is robust.

Why Other Options Are Wrong:
HP is not the odd pair because its letters are separated by 8 positions. FN is not the odd pair because its letters are again separated by 8 positions. RZ is not the odd pair because it also maintains the gap of 8 between letters. CJ is the odd pair because its letters are separated by a gap of 7 instead of 8.

Common Pitfalls:
Some learners may try to focus on the shapes or sounds of the letters rather than their exact positions, which does not help in this numeric pattern. Another common mistake is inaccurate counting between letters, especially when near the end of the alphabet. To avoid such errors, always use the numeric positions explicitly and perform the subtraction carefully for each pair.

Final Answer:
The letter pair that does not have a gap of 8 between its letters and is therefore the odd one out is CJ.