In this letter pair analogy, “MRQ is to PUT as ______ is to ______”. Choose the option where the second group is formed from the first by the same alphabet shift used in MRQ to get PUT.

Introduction / Context:
This analogy uses a constant shift in the alphabet to transform one group of letters into another. The example pair is “MRQ : PUT”. We must determine the exact shift pattern and then select the option where the same shift is applied from the first group of letters to the second. This tests letter coding skills and attention to consistent position changes.

Given Data / Assumptions:

• Example: MRQ → PUT. • Options: NOT : MNS, FRY : IUB, PEG : RGI, SAP : QYN. • Alphabet positions: A = 1, B = 2, ..., Z = 26. • We expect a single constant shift (likely +3) applied to each letter.

Concept / Approach:
We compare the positions of M, R, and Q with those of P, U, and T. If the difference is the same for all three letters, we have identified the transformation rule. We then test each option pair to see which one uses that very rule between its first and second groups. The correct pair will be the one where every corresponding letter is shifted by the same amount as in MRQ → PUT.

Step-by-Step Solution:
Step 1: Convert MRQ and PUT to numeric positions. M = 13, R = 18, Q = 17. P = 16, U = 21, T = 20. Step 2: Compute the shifts. 13 → 16: +3; 18 → 21: +3; 17 → 20: +3. So the rule is “add 3 to each letter”. Step 3: Test option B: FRY → IUB. F = 6 → I = 9 (+3). R = 18 → U = 21 (+3). Y = 25 → B = 2 (25 + 3 = 28; 28 − 26 = 2, wrapping around to B). This pair exactly follows the +3 rule, including proper wrap around. Step 4: Briefly test the other options and observe they do not consistently use +3 shifts for all letters.

Verification / Alternative check:
To verify option B further, we can apply the inverse operation (−3) to IUB. I (9) − 3 = F (6), U (21) − 3 = R (18), B (2) − 3 = 29, and 29 − 26 = 3 → C, but we expect Y (25). Noticing that we misapplied the wrap around, we should instead think: starting from Y (25), adding 3 gives 28; 28 − 26 = 2 (B). Reversing from B, subtract 3: 2 − 3 = −1; add 26 to stay in the alphabet: 25 → Y. This confirms complete reversibility of the +3 mapping. The same reversible structure appears in MRQ : PUT when subtracting 3 from P, U, and T to return to M, R, and Q.

Why Other Options Are Wrong:
• NOT : MNS – involves a mixture of forward and backward shifts; does not maintain a constant +3 pattern. • PEG : RGI – differences in positions are not uniformly +3 for P → R, E → G, and G → I. • SAP : QYN – again, the shift values vary and do not consistently equal +3.

Common Pitfalls:
Candidates sometimes check only one or two letters in a pair and ignore the rest. Another common error is mishandling wrap around when letters go beyond Z. Always verify that all three letters follow the same shift and handle any overflow by subtracting 26 to stay within A–Z. Doing this carefully shows that FRY : IUB is the only pair with a uniform +3 shift in all positions, just like MRQ : PUT.

Final Answer:
The letter pair that correctly completes the analogy is FRY : IUB.