Understanding the Letter Pair Pattern

The question asks us to identify a pair of letter sets that follows the same logical pattern as the two given examples: ARH: YOJ and SFP: QCR. This is a type of analogy or coding-decoding problem that requires finding a consistent rule connecting the letters in each pair.

Decoding the Pattern: ARH to YOJ

First, let's analyze the relationship between the letters in the first pair, ARH: YOJ. We can do this by assigning numerical positions to each letter based on their order in the alphabet (A=1, B=2, ..., Z=26) and finding the difference between the corresponding letters.

• First Letter: A is the 1^st letter, and Y is the 25^th letter. The shift from A to Y can be seen as moving 2 positions backward in the alphabet (A \(\rightarrow\) Z \(\rightarrow\) Y). Mathematically, this is \(1 - 2 = -1\), which corresponds to the 25^th position (Y) when wrapping around from Z. Or, \(25 - 1 = +24\). Let's use the backward shift: -2.
• Second Letter: R is the 18^th letter, and O is the 15^th letter. The shift is \(15 - 18 = -3\).
• Third Letter: H is the 8^th letter, and J is the 10^th letter. The shift is \(10 - 8 = +2\).

Based on ARH: YOJ, the pattern appears to be: (-2, -3, +2) applied to the letter positions.

Verifying the Pattern: SFP to QCR

Next, we must verify if this pattern (-2, -3, +2) holds true for the second given pair, SFP: QCR.

• First Letter: S is the 19^th letter. Q is the 17^th letter. The shift is \(17 - 19 = -2\). This matches our pattern.
• Second Letter: F is the 6^th letter. C is the 3^rd letter. The shift is \(3 - 6 = -3\). This also matches our pattern.
• Third Letter: P is the 16^th letter. R is the 18^th letter. The shift is \(18 - 16 = +2\). This matches our pattern as well.

Since the pattern (-2, -3, +2) is consistent across both examples, we can confidently use it to evaluate the options.

Applying the Pattern to Find the Correct Option

Now, let's test each option against the established pattern (-2, -3, +2).

Option 1: QPV: OLP

• Q (17) \(\rightarrow\) O (15): \(15 - 17 = -2\). (Matches)
• P (16) \(\rightarrow\) L (12): \(12 - 16 = -4\). (Does not match -3)
• V (22) \(\rightarrow\) P (16): \(16 - 22 = -6\). (Does not match +2)

This option does not follow the pattern.

Option 2: FTH : BNZ

• F (6) \(\rightarrow\) B (2): \(2 - 6 = -4\). (Does not match -2)
• T (20) \(\rightarrow\) N (14): \(14 - 20 = -6\). (Does not match -3)
• H (8) \(\rightarrow\) Z (26): \(26 - 8 = +18\). (Does not match +2)

This option does not follow the pattern.

Option 3: WLL: UIN

• W (23) \(\rightarrow\) U (21): \(21 - 23 = -2\). (Matches)
• L (12) \(\rightarrow\) I (9): \(9 - 12 = -3\). (Matches)
• L (12) \(\rightarrow\) N (14): \(14 - 12 = +2\). (Matches)

This option perfectly matches the pattern (-2, -3, +2).

Option 4: WBN:YFT

• W (23) \(\rightarrow\) Y (25): \(25 - 23 = +2\). (Does not match -2)
• B (2) \(\rightarrow\) F (6): \(6 - 2 = +4\). (Does not match -3)
• N (14) \(\rightarrow\) T (20): \(20 - 14 = +6\). (Does not match +2)

This option does not follow the pattern.

Conclusion

By applying the identified pattern of positional shifts (-2, -3, +2) to each letter, we found that only the pair WLL: UIN consistently follows the same logic as the given examples ARH: YOJ and SFP: QCR.