In the following letter analogy, FS is related to LY in a certain way. Using the same alphabetical pattern, IV is related to which of the following letter pairs?

Introduction / Context:
This question involves a simple but important letter analogy based on adding a fixed number to the positions of letters in the alphabet. The pair FS and LY reveals a transformation rule that must be applied to IV to find the correct related pair. Being comfortable with letter positions and constant shifts is crucial for many codes and analogies in verbal reasoning sections.

Given Data / Assumptions:

• First pair of letter groups: FS : LY
• Second first term: IV
• We work with English alphabet positions A equal to 1 through Z equal to 26.
• We need the same transformation that maps FS to LY to map IV to the correct option.

Concept / Approach:
The usual approach is to convert both FS and LY into their numeric positions and examine the difference between corresponding letters. If we get a constant increment or decrement, that becomes the rule. Then we will apply this shift to the letters I and V. Since we are dealing with two letter groups, the same shift should apply to both letters independently.

Step-by-Step Solution:
Step 1: Convert FS to positions. F is 6 and S is 19. Step 2: Convert LY to positions. L is 12 and Y is 25. Step 3: Find the change from F to L. The difference is 12 minus 6, which equals plus 6. Step 4: Find the change from S to Y. The difference is 25 minus 19, which also equals plus 6. Step 5: Conclude that the rule is to add 6 to the position of each letter in the pair. Step 6: Apply the same rule to IV. Positions: I is 9 and V is 22. Step 7: Add 6 to each. I plus 6 gives 15, which is O. V plus 6 gives 28, which wraps around the alphabet as 2 (since 28 minus 26 equals 2), corresponding to letter B. Step 8: Combine these letters to obtain OB.

Verification / Alternative check:
We can verify the wraparound step separately. After Z which has position 26, we start again at A as 1, B as 2, and so on. So position 28 is the same as position 2, which is B. Thus I goes to O and V goes to B under the plus six rule. The original mapping from F to L and from S to Y also matches this rule. Therefore FS : LY and IV : OB follow the same alphabetic transformation.

Why Other Options Are Wrong:
Option GT would require subtracting 2 from each letter of IV, which does not match the plus six rule found from FS to LY. Option HS uses mixed changes which are not constant. Option TZ likewise does not result from adding six to I and V because I plus six is not T and V plus six is not Z without an inconsistent adjustment. Since the analogy demands a single consistent rule, all these alternatives are incorrect.

Common Pitfalls:
A common mistake is ignoring the circular nature of the alphabet and assuming that adding a number that exceeds 26 is impossible. Another mistake is to focus only on the first letter mapping and not confirm the transformation for the second letter. To solve such questions reliably, always compute numeric positions, apply the rule carefully, and handle wraparound by subtracting 26 when the position exceeds 26.

Final Answer:
The pair of letters that completes the analogy FS : LY :: IV : ? is OB.