In this letter analogy, “BFJ is to NRV as DHL is to ______”. Choose the group of letters that completes the analogy by using the same fixed forward alphabet shift on each letter.

Introduction / Context:
This reasoning question presents a letter coding pattern where each letter in the group BFJ is shifted forward by a constant number of positions to obtain NRV. The task is to identify that shift and then apply it to the second group DHL to complete the analogy. Such problems test your ability to work efficiently with alphabet positions and detect hidden arithmetic patterns between them.

Given Data / Assumptions:

• Example mapping: BFJ → NRV. • Target mapping: DHL → ? • Options: PTA, PTX, KQS, MQV. • Alphabet positions: A = 1, B = 2, ..., Z = 26.

Concept / Approach:
We compare each corresponding letter of BFJ and NRV to find how many positions forward in the alphabet each letter moves. If the difference is the same for all positions, we have a single constant shift. Once that shift is determined, we apply it to the letters in DHL. The correct answer will be the option that exactly matches the resulting letters in their correct order.

Step-by-Step Solution:
Step 1: Convert BFJ and NRV to numeric positions. B = 2, F = 6, J = 10. N = 14, R = 18, V = 22. Step 2: Calculate the shifts. 2 → 14: +12. 6 → 18: +12. 10 → 22: +12. So the rule is “add 12 to each letter”. Step 3: Apply the same rule to DHL. D = 4, H = 8, L = 12. Add 12: 4 + 12 = 16 → P, 8 + 12 = 20 → T, 12 + 12 = 24 → X. Step 4: The resulting letters are P T X (PTX).

Verification / Alternative check:
Check the reverse mapping from NRV to BFJ by subtracting 12: N (14) − 12 = B (2), R (18) − 12 = F (6), V (22) − 12 = J (10). The mapping is perfectly reversible, confirming a consistent shift of 12. Applying the same subtraction to PTX leads back to DHL: P (16) − 12 = D (4), T (20) − 12 = H (8), X (24) − 12 = L (12). This shows that we have applied the correct rule and that PTX is the valid output.

Why Other Options Are Wrong:
• PTA: The letters P, T, and A do not all arise from adding 12 to D, H, and L respectively; A would require a wrap around that is not part of this mapping. • KQS and MQV: These sequences do not correspond to a uniform +12 shift on DHL and break the relationship demonstrated by BFJ and NRV.

Common Pitfalls:
A frequent error is to miscount the shift or to assume a smaller shift like +10 without checking all letters. Another mistake is to look only at the first letter and pick an option that shares that letter but does not match the pattern in the remaining positions. Always verify the shift for each letter in the example pair and ensure the same shift can be applied consistently in the new pair.

Final Answer:
The letter group that correctly completes the analogy is PTX.