In the following letter analogy question, LK is related to OP in a particular way. Using the same pattern, which pair of letters should complete the analogy LK : OP :: ? : UV?

Introduction / Context:
This question is a letter based analogy where we must discover the alphabetic pattern that links one pair of letters to another. Once we understand how LK is related to OP, we apply the same rule to find the pair that will be related to UV in an identical way. Letter analogy questions like this test understanding of letter positions and consistent shifts in the English alphabet.

Given Data / Assumptions:
We are given the pair LK : OP. We must choose a pair ? so that LK : OP :: ? : UV. All letters are capital English letters from A to Z. The same relationship must hold between both pairs.

Concept / Approach:
A reliable method is to convert letters to their numerical positions in the alphabet. Then we look for how many steps forward we move from the first letter pair to the second. When we identify a simple, consistent shift, we use that shift again to construct the missing pair that will correspond to UV. The aim is to find a rule that works neatly and symmetrically for both pairs.

Step-by-Step Solution:
Step 1: Write down positions for L and K. L is the 12th letter, K is the 11th letter. Step 2: Write down positions for O and P. O is the 15th letter, P is the 16th letter. Step 3: Observe the shifts. L (12) to O (15) is a shift of +3. K (11) to P (16) is a shift of +5. The key idea is that the two letters of the first pair are consecutive in reverse order (L, K), while the two letters of the second pair are consecutive in normal order (O, P) and are three positions ahead in the alphabet. Step 4: Now focus on the second pair involving UV. U and V are consecutive letters in the normal forward order, just like O and P. To match the pattern, the unknown pair should also be two consecutive letters that appear three positions before U and V. Step 5: Move three steps back from U and V. U is the 21st letter. Three positions back gives 18, which is R. V is the 22nd letter. Three positions back gives 19, which is S. Therefore the required pair is RS.

Verification / Alternative check:
If we now check RS and UV: R and S are consecutive letters, just like L and K, and U and V are also consecutive letters, just like O and P. Additionally, U and V are exactly three positions after R and S in the alphabet, which mirrors the three step forward shift seen from L to O. This shows that the structure of the relation is consistent across both pairs, so RS is the only pair that satisfies the requirement.

Why Other Options Are Wrong:
KL are consecutive letters, but if we move three positions forward from K and L, we do not arrive at U and V. QR are consecutive, but three positions ahead of Q and R are T and U, not U and V. WX are consecutive letters located after U and V, so they cannot generate UV by shifting forward. PQ are consecutive letters, but three positions ahead of P and Q are S and T, which again does not match UV.

Common Pitfalls:
Many learners only check whether both pairs contain consecutive letters and ignore the exact number of positions between them. Others may try to apply a single constant shift to both letters without considering that the pattern can involve relative placement of pairs in the alphabet. It is important to look at both consecutiveness and the distance between the pairs. Checking the pattern carefully for all letters helps avoid incorrect guesses based on partial similarities.

Final Answer:
The pair of letters that correctly completes the analogy is RS.