In the series HK, ?, PQ, TT, XW, which pair of letters should replace the question mark so that the pattern in both positions is preserved?

Introduction / Context:
This problem shows a series of alphabet pairs: HK, ?, PQ, TT, XW. We need to identify the missing pair in the second position so that the pattern in the first and second letters remains consistent throughout the series. Each letter pair is drawn from the English alphabet, and the pattern is hidden in the numeric positions and the step sizes between successive letters. This type of question helps train candidates to detect separate series within the first and second positions of each pair.

Given Data / Assumptions:

• Series: HK, ?, PQ, TT, XW.• First letters in order: H, ?, P, T, X.• Second letters in order: K, ?, Q, T, W.• Alphabet positions: A=1, B=2, ..., Z=26.• We assume a simple numeric pattern for each of the two sub series.

Concept / Approach:
The strategy is to analyse the first letters as a numeric series, then do the same for the second letters. Often, each sub series follows a fixed difference, such as +4 or +3, which is easier to see when the letters are converted into numbers. Once the pattern is known for both positions, we can deduce the missing letters that make the series consistent from start to end.

Step-by-Step Solution:
Step 1: First letters: H, ?, P, T, X.Step 2: Convert to positions where possible: H=8, P=16, T=20, X=24.Step 3: Examine differences between the known terms: 16 − 8 = 8 and 20 − 16 = 4, 24 − 20 = 4.Step 4: Noticing that P, T and X are evenly spaced by +4 (16 → 20 → 24), we can suspect a simpler pattern: ? might be 12 so that the first letters progress as 8, 12, 16, 20, 24, which all differ by +4.Step 5: Position 12 corresponds to L, so the missing first letter should be L.Step 6: Now analyse second letters: K, ?, Q, T, W.Step 7: Convert known letters: K=11, Q=17, T=20, W=23.Step 8: Differences: 17 − 11 = 6, 20 − 17 = 3, 23 − 20 = 3.Step 9: The last three form 11, 14, 17, 20, 23 if we assume the missing second letter is 14, with constant +3 from 11 to 14 to 17 to 20 to 23.Step 10: Position 14 is N, so the missing second letter is N.Step 11: Therefore, the missing pair is LN.

Verification / Alternative check:
Write the full series with the discovered term: HK, LN, PQ, TT, XW. The first letters H(8), L(12), P(16), T(20), X(24) clearly form an arithmetic progression with common difference +4. The second letters K(11), N(14), Q(17), T(20), W(23) form an arithmetic progression with common difference +3. This dual arithmetic structure confirms that the series is consistent and that LN is the only pair that fits both patterns at the same time.

Why Other Options Are Wrong:
NO, LK and NM all fail one or both of the arithmetic progressions. For example, if we choose NO (N=14, O=15), the first letters become H(8), N(14), P(16), T(20), X(24), where the difference 14 − 8 = 6 breaks the +4 rule. Similarly, second letters would not maintain the +3 pattern. LK and NM introduce mismatches either in the first letter series or in the second letter series, so they cannot be accepted as correct completions of the pattern.

Common Pitfalls:
Some candidates may only check whether the missing pair is somewhere numerically between HK and PQ and then guess without verifying the exact arithmetic steps. Others focus solely on first letters and overlook the fact that second letters usually follow their own consistent pattern. Reliable solutions require checking that the same difference holds throughout the entire sequence for both positions, rather than relying on approximate spacing or visual intuition.

Final Answer:
LN