In the letter series _ B A _ B B A _ A B _ B, which one set of letters, when placed sequentially in the blanks, will correctly complete the pattern?

Introduction / Context:
This missing letter series involves only two letters, A and B, with several blanks. Even though the alphabet set is small, the pattern can still be quite structured. The question aims to test your ability to recognise not only the order of letters but also how the lengths of consecutive runs of A and B may change in a systematic way across the series.

Given Data / Assumptions:

• The incomplete sequence is: _ B A _ B B A _ A B _ B.
• There are four blanks to be filled in order.
• Options provide four letter strings that must be inserted exactly as given.
• The completed series is expected to reflect an orderly growth in the lengths of runs of the same letter.

Concept / Approach:
For a two letter series like this, a useful idea is to look for patterns in the number of consecutive A or B letters. One elegant design is to have run lengths that increase gradually, for example A once, then B once, then A twice, B twice, A three times, and B three times. We test each option by filling the blanks and then computing run lengths of A and B. The correct option should reveal a simple and increasing pattern in these runs.

Step-by-Step Solution:
Step 1: The blanks are at positions 1, 4, 8, and 11. Step 2: Insert the letters from option B, that is A A A B, into these blanks. Step 3: The full series becomes: A B A A B B A A A B B B. Step 4: Group consecutive identical letters: A, B, A A, B B, A A A, B B B. Step 5: The run lengths are thus 1 A, 1 B, 2 A, 2 B, 3 A, 3 B. Step 6: This sequence of run lengths (1, 1, 2, 2, 3, 3) is very regular and clearly intentional.

Verification / Alternative check:
To verify, consider whether any other option yields such a neat pattern. With option B, every time the letter changes from A to B or B to A, the length of the new run either remains the same initially or increases by one at the correct positions. The result is a simple and memorable structure where each letter appears in runs that grow from 1 to 3. No other option produces this elegant progression, confirming that option B is the right answer.

Why Other Options Are Wrong:
Option A (ABAB) gives run lengths that jump irregularly and do not follow the 1, 1, 2, 2, 3, 3 pattern. Option C (BBAB) starts with a double B at the beginning and disrupts the balanced alternation of A and B runs. Option D (BBBA) also creates long runs at unexpected positions and prevents the simple increasing structure. Because these options fail to generate a smooth pattern in the sizes of A and B segments, they cannot be accepted as correct completions of the series.

Common Pitfalls:
One common mistake is to look only at which letter should appear in each blank based on the immediate neighbours, without considering how long each sequence of identical letters should be. Another error is to choose an option that appears visually symmetrical but lacks a consistent rule in run lengths. For two letter series, always count the sizes of consecutive groups of the same letter and see if these lengths follow a simple law such as constant steps or gradual growth.

Final Answer:
The correct set of letters is option B, AAAB, resulting in runs of A and B with lengths 1, 1, 2, 2, 3, 3.