In this letter analogy question, TR is related to VX, so you must select the pair of letters that stands in the same relation to MK from the given alternatives.

Introduction / Context:

This question is a two-letter analogy based on positions in the English alphabet. The pair "TR : VX" is formed by shifting each letter of the first pair by a certain number of positions to obtain the second pair. Your task is to recognise this pattern and apply it to the pair "MK" in order to find the corresponding pair from the options.

Given Data / Assumptions:

- First analogy pair: TR and VX.
- Second pair to complete: MK and ?.
- Alphabet positions: A = 1, B = 2, ..., Z = 26.
- Options are QP, QR, OQ, OP and NR.
- The same transformation that converts TR to VX must be used to convert MK to the correct answer.

Concept / Approach:

The usual technique with letter analogies is to convert each letter to its numeric position, find the shift for each letter in the first pair, and then apply the same shifts to the second pair. We will examine how T changes to V and how R changes to X, then use those observed increments to transform M and K. Only the option that exactly matches the resulting letters can be the correct answer.

Step-by-Step Solution:

Verification / Alternative check:

To verify, quickly test whether any other option could fit the observed pattern. Suppose we choose OP: that would give M to O (+2) and K to P (+5), which does not match the +6 shift for the second letter observed in the TR to VX mapping. Similarly, QP or QR require different shifts for one or both letters, violating the consistency of the analogy. Only OQ gives the exact +2 and +6 increments for the first and second letters respectively, fully matching the original pattern.

Why Other Options Are Wrong:

QP would require M to become Q (+4) and K to become P (+5), which does not follow the +2, +6 pattern.

QR would correspond to shifts of +4 and +7 respectively, again inconsistent with the established mapping from TR to VX.

OP arises from shifts of +2 for M and +5 for K, which does not match the second letter shift of +6 seen in the first pair.

NR would represent shifts of +1 and +7, which are not observed in the transformation from TR to VX and thus cannot be correct.

Common Pitfalls:

A common pitfall in such questions is to guess based on rough similarity rather than precise numeric shifts. Some students notice that many options are alphabetically near one another and choose one that superficially seems close. However, letter analogy questions require exact mapping. Another mistake is to assume the same shift for both letters when the first pair clearly shows different shifts for each position.

Final Answer:

Applying the same +2 and +6 shifts that map TR to VX, the pair MK becomes OQ.