In the alphabet series IB, QD, XH, DP, which pair of letters should come next so that the same pattern continues throughout the series?

Introduction / Context:
This question presents a slightly more complex alphabet pair series: IB, QD, XH, DP, ?. The task is to determine which pair of letters should come next so that the underlying pattern is maintained. Each pair represents two interconnected sub series evolving according to different rules. Such questions test a deeper level of pattern recognition, including the ability to handle varying increments and cyclic movement through the alphabet in both forward and backward directions.

Given Data / Assumptions:

• Known pairs: IB, QD, XH, DP, ?.• First letters form the series: I, Q, X, D, ?.• Second letters form the series: B, D, H, P, ?.• Alphabet positions: A=1, B=2, ..., Z=26, with wrap around when needed.• We expect regular numeric rules in both first and second letter sequences.

Concept / Approach:
We treat each letter as a number and compute the differences between successive first letters, then between successive second letters. The first letters often follow one arithmetic pattern, and the second letters another. When the differences themselves decrease or increase in a regular way, this indicates that the pattern is based on changing steps, not just a fixed increment. We then extend those step patterns to predict the next letter in each sub series.

Step-by-Step Solution:
Step 1: Convert first letters to positions: I=9, Q=17, X=24, D=4.Step 2: Compute the forward cyclic differences:• 9 to 17: +8• 17 to 24: +7• 24 to 4: +6 (since 24 + 6 = 30 and 30 − 26 = 4)Step 3: The pattern for first letters uses step sizes that decrease by 1 each time: +8, +7, +6. The next step should be +5.Step 4: Apply +5 to D (4): 4 + 5 = 9, which corresponds to I. So the next first letter is I.Step 5: Now examine the second letters: B=2, D=4, H=8, P=16.Step 6: Compute the differences:• 2 to 4: +2• 4 to 8: +4• 8 to 16: +8Step 7: Here the steps double each time: +2, +4, +8. The next step should be +16.Step 8: Apply +16 to P (16): 16 + 16 = 32, and 32 − 26 = 6, which corresponds to F.Step 9: Therefore, the next pair in the series is IF.

Verification / Alternative check:
We can summarise the pattern for first letters as a sequence of step sizes decreasing from +8 to +5, and for second letters as step sizes increasing by powers of two. Specifically, the first letters follow I (9) → Q (17) → X (24) → D (4) → I (9) with steps +8, +7, +6, +5 cyclically. The second letters follow B (2) → D (4) → H (8) → P (16) → F (6) with steps +2, +4, +8, +16 cyclically. This dual pattern is internally consistent and explains each term of the series, validating IF as the correct continuation.

Why Other Options Are Wrong:
KL, KI and GH do not match both patterns simultaneously. For example, choosing KI would provide the correct first letter I but an incorrect second letter I=9, which is not obtained by adding +16 to P=16. Similarly, GH and KL do not arise from the systematic step changes found in the first and second letter sub series. Since the numeric rules are strict and clear, only IF satisfies both conditions at the same time.

Common Pitfalls:
Some candidates identify only one of the two patterns, for example the decreasing steps in the first letters, and then guess a second letter that seems visually plausible. Others may forget to treat the alphabet cyclically and miscalculate differences when letters move past Z. To avoid mistakes, always compute all differences carefully, check for simple numeric sequences in the step sizes and ensure that the chosen answer fits every identified rule for both letters in the pair.

Final Answer:
IF