A letter pair series is given, with the first term missing. Choose the correct alternative from the given options that will complete the series ?, YV, BY, FC.

Difficulty: Medium

Correct Answer: WT

Explanation:


Introduction / Context:
This question presents a series of two letter terms where the first term is missing. We must detect the pattern from the remaining three terms and work backwards to find the missing initial pair. In alphabet series problems, working from right to left using the same logic is often as valid as progressing from left to right.


Given Data / Assumptions:

  • The visible terms are YV, BY, FC.
  • We must find the pair that precedes YV in the series.
  • Each item consists of two uppercase letters.
  • Alphabet positions are taken from A = 1 through Z = 26.


Concept / Approach:
We analyse the first letters as one subsequence and the second letters as another. We calculate the differences between consecutive terms from left to right and identify a pattern. Then we extrapolate backwards to determine the missing first term. This question uses increasing step sizes, so recognising that pattern is the key.


Step-by-Step Solution:
Step 1: Look at the first letters of the known terms: Y, B, F. Step 2: Positions are Y = 25, B = 2, F = 6. The move from Y (25) to B (2) is effectively plus 3 when considered cyclically, since 25 plus 3 equals 28 and 28 minus 26 equals 2. The move from B (2) to F (6) is plus 4. Step 3: This suggests that the steps in the first letter positions could be plus 2, plus 3, plus 4, and so on. Step 4: Let the unknown first letter have position x. Then moving plus 2 should give 25 for Y. So x plus 2 equals 25, which implies x equals 23, corresponding to the letter W. Step 5: Now consider the second letters of the known terms: V, Y, C. Step 6: Their positions are V = 22, Y = 25, C = 3. From V (22) to Y (25) is plus 3. From Y (25) to C (3) is plus 4 cyclically, since 25 plus 4 equals 29 and 29 minus 26 equals 3. Step 7: The pattern is again plus 2, plus 3, plus 4 for the second letters. So let the unknown second letter have position y. Then y plus 2 must equal 22 (position of V), giving y equals 20, which is T. Step 8: Therefore, the missing first term is WT.


Verification / Alternative check:
We can re write the full series as WT, YV, BY, FC. The first letters W (23), Y (25), B (2), and F (6) increase by plus 2, plus 3, plus 4 cyclically. The second letters T (20), V (22), Y (25), and C (3) also increase by plus 2, plus 3, plus 4 cyclically. This confirms the pattern and validates WT as the only correct missing term.


Why Other Options Are Wrong:
Pairs MN, VS, and XU do not satisfy the required plus 2 step leading into YV for both the first and second letters. For example, XU would give incorrect forward differences when compared to YV. None of these choices preserve the structured increment pattern in both positions, so they must be rejected.


Common Pitfalls:
Candidates sometimes try to solve such questions only from left to right and feel stuck when the first term is missing. Others ignore cyclic movement and miscalculate differences that cross from Z back to A. Recognising increasing step sizes and properly handling wrap around lets us solve such series reliably.


Final Answer:
The missing first term of the series is WT.

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