In this letter analogy, “ILN is to FIK as RUW is to ______”. Determine the group of letters that completes the analogy by following the same alphabet shift pattern.

Introduction / Context:
This question involves a simple but precise alphabet shift. We are given the pair “ILN : FIK” and must determine which option correctly represents the image of “RUW” under the same transformation. Letter based analogies like this test your ability to convert letters into their numeric positions and apply consistent forward or backward shifts.

Given Data / Assumptions:

• Known pair: ILN → FIK. • Unknown mapping: RUW → ? • Options: ORT, PSU, NQS, LNQ. • We treat the alphabet with A = 1, B = 2, ..., Z = 26 and assume a constant shift rule.

Concept / Approach:
To discover the pattern, we compare each letter in ILN with the corresponding letter in FIK. If the differences in their positions are consistent (for example, all letters move back by the same number), we use that same shift for every letter in RUW. Letter coding often uses such fixed shifts, which are easy to handle once the numeric positions are written out.

Step-by-Step Solution:
Step 1: Convert ILN into numbers. I = 9, L = 12, N = 14. Step 2: Convert FIK into numbers. F = 6, I = 9, K = 11. Step 3: Calculate the shift for each position. • 9 → 6: 9 − 3 = 6. • 12 → 9: 12 − 3 = 9. • 14 → 11: 14 − 3 = 11. All three letters are shifted backward by 3 positions in the alphabet. Step 4: Apply the same −3 shift to RUW. • R is 18; 18 − 3 = 15 → O. • U is 21; 21 − 3 = 18 → R. • W is 23; 23 − 3 = 20 → T. Step 5: The resulting sequence is O R T (ORT).

Verification / Alternative check:
We can quickly check that applying the inverse shift (+3) to ORT returns RUW. O (15) + 3 = 18 → R, R (18) + 3 = 21 → U, and T (20) + 3 = 23 → W. This exact reversibility confirms that −3 is the right shift and that ORT is the correct corresponding group. Any other option would fail this consistent +3 / −3 relationship.

Why Other Options Are Wrong:
• PSU: P (16), S (19), U (21) do not arise from subtracting 3 from R (18), U (21), W (23); their shifts are inconsistent. • NQS: N (14), Q (17), S (19) also do not match the uniform −3 rule. • LNQ: L (12), N (14), Q (17) again fails to follow the same transformation applied to ILN.

Common Pitfalls:
A typical mistake is to focus only on the first or last pair of letters and choose an option that matches those partially, without checking all three positions. Another error is to attempt variable shifts, even though a constant shift already fits perfectly. Always verify that your discovered rule works for every letter before finalising your answer.

Final Answer:
The group of letters that completes the analogy is ORT.