In the following letter series, a _ c a a b _ a _ b c a a b _ a _ b _ a, which one set of letters, when placed sequentially in the blanks, will correctly complete the series and maintain a consistent repeating pattern?

Introduction / Context:
This question tests the concept of letter series completion. A letter series is created according to a hidden pattern, and some positions are left blank. The task is to identify a single fixed sequence of letters that, when inserted in order into the blanks, restores a clean and consistent pattern across the entire series. Such problems are common in aptitude and competitive examinations because they check observation, pattern recognition, and systematic reasoning rather than mere memorisation.

Given Data / Assumptions:

• The given series is: a _ c a a b _ a _ b c a a b _ a _ b _ a.
• There are six blanks, and each option provides six letters to be placed sequentially in those blanks.
• Only one option should generate a neat, repeating or logically consistent pattern for the entire series.

Concept / Approach:
The most reliable approach is to treat the series as a possible repetition of a short block of letters. Many letter series questions are formed by repeating a small pattern like ABC, ABCAAB, or similar units. We first note the positions of the fixed letters and then see how they may fit into a repeating block. Once we suspect a base block, we check each option by filling the blanks and seeing whether the resulting full series decomposes into equal segments with the same order of letters throughout.

Step-by-Step Solution:
Step 1: Mark the blanks at positions 2, 7, 9, 15, 17, and 19 in the series. Step 2: Fill these six blanks with the letters from option B (b c a c a c) in order. Step 3: The completed series becomes: a b c a a b c a a b c a a b c a a b c a. Step 4: Group the completed series as: abcaab abcaab abcaab abca. Step 5: Observe that the pattern ABCAAB is consistently repeated three times, and the remaining part also follows the same order. Step 6: This shows that option B generates a clean and consistent repeating structure, which is the hallmark of a correct answer in such questions.

Verification / Alternative check:
We can verify our choice by checking whether any other option yields a similarly regular structure. When option B is used, the sequence of letters always appears in the same order, without any irregularity or break. This symmetry strongly indicates that we have identified the intended pattern. A quick secondary check is to see that no adjacent group violates the sequence a, b, c and that the distribution of each letter across the series is balanced in line with the repeating block. This cross check confirms that option B uniquely fits the series.

Why Other Options Are Wrong:
Option A (cbacba) produces clusters where the letters do not follow a simple, repeated order; some segments show disruptions and the entire string cannot be partitioned into identical blocks. Option C (acbaca) results in irregular transitions where the letters do not repeat in a fixed pattern and some local groups contradict the surrounding structure. Option D (bbacaa) creates consecutive duplicate letters at positions where the underlying structure expects a different symbol; the series then fails to maintain a single repeating block. Hence these options do not generate a clean, systematic arrangement.

Common Pitfalls:
Many learners try to fill blanks locally by matching only the immediate neighbours, without checking the full series after insertion. This can produce a small portion that looks right but fails when extended to the entire pattern. Another common mistake is to focus only on frequencies of letters rather than the precise order in which they appear. In letter series questions, the order of letters is more important than simple counts. It is therefore essential to verify the completed series globally rather than relying on partial matches.

Final Answer:
The correct set of letters that completes the series is option B, bcacac.