In the alphabet pair series ?, WX, AB, FG, which of the following pairs of letters should replace the question mark to complete the series logically?

Difficulty: Medium

Correct Answer: TU

Explanation:


Introduction / Context:
This question features a two letter alphabet series of the form ?, WX, AB, FG. We must determine which pair comes before WX so that the entire sequence shows a consistent pattern. The challenge lies in recognising that the alphabet can be treated cyclically from Z back to A, and that the jumps between the first letters and between the second letters follow a systematic progression rather than a random movement.


Given Data / Assumptions:

    • Known terms: ?, WX, AB, FG.• Each term is a pair of consecutive letters: W X, A B and F G.• First letters are: ?, W, A, F.• Second letters are: ?, X, B, G.• Alphabet positions: A=1, B=2, ..., Z=26, and we allow wrap around after Z.


Concept / Approach:
To find the missing pair, we study the pattern of the first letters only, then the second letters only. Because the series wraps around the end of the alphabet, we interpret increments modulo 26. We are particularly interested in whether the steps between successive terms themselves follow a pattern, such as increasing by 1 each time, and we then extend that rule backward to reveal the unknown term at the beginning.


Step-by-Step Solution:
Step 1: Work with first letters: W, A, F.Step 2: Convert to positions: W=23, A=1, F=6.Step 3: From W to A: 23 to 1 is an increase of 4 if we move forward cyclically (23 + 4 = 27, and 27 − 26 = 1).Step 4: From A to F: 1 to 6 is an increase of 5.Step 5: This suggests a pattern of increments +4, +5. To extend it backward, we assume the previous increment was +3.Step 6: Let the unknown first letter be x. Then x + 3 = 23, so x = 20, which is T.Step 7: Now consider second letters: X=24, B=2, G=7.Step 8: From X to B: 24 to 2 is again +4 forward cyclically (24 + 4 = 28, and 28 − 26 = 2).Step 9: From B to G: 2 to 7 is +5, matching the same pattern.Step 10: Using +3 as the preceding increment, let the unknown second letter be y such that y + 3 = 24. Then y = 21, which is U.Step 11: Therefore, the missing pair at the beginning of the series is TU.


Verification / Alternative check:
Write the full series including TU: TU, WX, AB, FG. In numeric terms, the first letters T(20), W(23), A(1), F(6) progress with increments +3, +4, +5 (with wrap around from Z to A). The same is true for the second letters U(21), X(24), B(2), G(7). This repeated pattern of increasing differences confirms that the logic is symmetric for both positions and that TU is the unique valid missing term.


Why Other Options Are Wrong:
XW, PQ and UV do not create the required +3, +4, +5 progression. For example, if we choose PQ, the jump from P to W does not match the pattern seen from W to A and A to F. UV also leads to mismatched increments when compared with the known terms. Only TU aligns perfectly with the evolving step sizes in both components of the pair series.


Common Pitfalls:
One common mistake is to treat the alphabet as non cyclic and therefore miscalculate differences across the Z to A boundary. Another is to look only at the first letters or only at the second letters but not both, which can lead to a misleading partial pattern. For robust solutions, always check the entire series in both positions and account for circular movement when letters pass Z and restart at A.


Final Answer:
TU

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