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

Introduction / Context:

This is a letter analogy problem that checks your ability to observe patterns involving simple transformations like reversing pairs and shifting letters. The given pair is "TC : EV", and you need to determine which option forms a similar relationship with the pair "NS". A careful look at letter positions and order reveals the rule used to generate the second pair from the first.

Given Data / Assumptions:

- First pair: TC becomes EV.
- Second pair to be completed: NS becomes ?.
- Alphabet positions: A = 1, B = 2, ..., Z = 26.
- Options: QT, LK, PU, UP and RV.
- We assume the same pattern is applied to both letter pairs.

Concept / Approach:

One useful strategy in two-letter analogies is to check whether the letters are reversed and then shifted by a fixed number of positions. When we examine "TC" and "EV", we can see that if we first reverse TC to get CT and then move each letter forward by 2 positions, we obtain EV. We will verify this and then apply the same two-step operation to the pair NS.

Step-by-Step Solution:

Verification / Alternative check:

We can quickly check other options to ensure no other pair follows the same transformation. For NS, any correct option must be obtained by reversing NS to SN and then shifting each letter two steps ahead. Only U and P satisfy this condition. Pairs like QT, LK, PU and RV do not match the exact letters obtained in this process. Therefore, UP is uniquely consistent with the discovered rule, confirming the answer.

Why Other Options Are Wrong:

QT would require different shifts or a different ordering that does not align with the reverse-and-shift pattern used for TC.

LK is not derived from NS by reversing and then shifting forward by two positions, so it breaks the analogy.

PU has the correct letters but in the wrong order, indicating that the full pattern, including reversal, is not satisfied.

RV introduces letters that require larger or unequal shifts and does not follow the simple two-step transformation identified.

Common Pitfalls:

A common error is to observe only the shift in positions without noticing the reversal of letters. Another pitfall is to choose options that contain similar letters but ignore their precise order and exact positional changes. For success in such questions, always examine both the order and the numerical shifts carefully.

Final Answer:

Using the rule "reverse the pair and then shift each letter two positions forward", NS corresponds to UP.