In the following series of letter pairs, one pair is missing. Choose the pair that best completes the pattern: NM, PK, SI, ?

Introduction / Context:
This problem presents a sequence of letter pairs that changes in a specific, predictable way. Your job is to identify that pattern and extend it to find the next pair. Letter pair questions like this check your familiarity with alphabet positions and your ability to spot progressively changing differences.

Given Data / Assumptions:

• Given pairs: NM, PK, SI, ? • We assume A = 1, B = 2, ..., Z = 26. • The first letters follow one numeric pattern and the second letters follow another, both consistent. • Movement may be forward or backward by different step sizes.

Concept / Approach:
We separate the first letters (N, P, S, ...) and second letters (M, K, I, ...). We then convert them into numbers and study the differences between consecutive terms. Often in such series, the jump size itself grows or shrinks in a simple way. Once we identify this change in steps, we can easily compute the next term in each sequence.

Step-by-Step Solution:
Step 1: Consider the first letters: N, P, S. Numerical positions: N = 14, P = 16, S = 19. Differences: 14 → 16 is +2, 16 → 19 is +3. The increment is increasing by 1 each step. So the next increment should be +4: 19 + 4 = 23, which is W. Step 2: Consider the second letters: M, K, I. Numerical positions: M = 13, K = 11, I = 9. Differences: 13 → 11 is −2, 11 → 9 is −2. So we consistently subtract 2. Apply again: 9 − 2 = 7, which is G. Step 3: Combine both results. The missing pair is WG.

Verification / Alternative check:
Write the full numeric sequence: first letters 14, 16, 19, 23; second letters 13, 11, 9, 7. The first series uses increments +2, +3, +4, while the second series uses a constant decrement of −2. This dual pattern explains all given terms and leads uniquely to WG. None of the other options matches these exact movements for both letters.

Why Other Options Are Wrong:
• VE: V is 22, which would mean an increment of only +3 from S instead of +4. E is 5, which does not match the constant −2 pattern from I. • WF: W is correct for the first letter, but F is 6 not 7, so the second letter sequence would be broken. • VG: G as second letter is correct, but V as first letter would require a different increment than the one dictated by the growing pattern.

Common Pitfalls:
A typical error is to assume the same constant step size for both letters, or to ignore that the increment for the first letters is changing. Another mistake is to check only approximate distances instead of computing exact numerical positions. Systematic calculation is the safest way to avoid such traps.

Final Answer:
The pair that correctly continues the series is WG.