Understanding and completing letter series is a common type of logical reasoning question. These questions test your ability to identify patterns and rules governing a sequence of letters.

Analyzing the Given Letter Series

The given letter series is:

d _ n _ b _ d a _ t b _ d a n _ b v

There are blanks in the series, and we need to find the correct combination of letters from the options to fill these blanks and complete the pattern.

Let's analyze the structure of the series and the placement of the given letters and blanks. The total number of positions (letters + blanks) is 22.

Identifying the Pattern in the Letter Series

To complete the letter series, we should look for repeating blocks or sequences of letters. Let's try inserting the letters from the options into the blanks to see if a clear pattern emerges.

Consider the second option, which provides the sequence 'a t v n v t'. Let's place these letters into the blanks:

Original Series: d _ n _ b _ d a _ t b _ d a n _ b v
Letters from Option 2: a t v n v t

Inserting these letters into the blanks gives:

d a n t b v d a n t b v d a n t b v

Let's rewrite this completed series:

dantbv dantbv dantbv

Looking at the completed series, we can clearly see a repeating block of letters: 'dantbv'. This block is repeated three times to form the complete series.

Verifying the Pattern with the Original Series and Option 2

Let's break down the completed series based on the repeating block 'dantbv':

• Block 1: d a n t b v
• Block 2: d a n t b v
• Block 3: d a n t b v

Now, let's compare this with the original series and the letters from Option 2:

The table shows that when the letters 'a t v n v t' are inserted into the blanks, the resulting series perfectly matches the repeating pattern 'dantbv' repeated twice. Wait, the original series has 16 letters and 6 blanks, total 22 positions. Let's recount.

d _ n _ b _ d a _ t b _ d a n _ b v (16 letters, 6 blanks = 22 positions total)

If the repeating block is 'dantbv' (6 letters), then 22 positions doesn't fit nicely. Let's re-examine the series structure with the inserted option 2: `d a n t b v d a n t b v d a n t b v`. This version is 18 characters long (12 letters + 6 blanks). However, the question says 16 letters are present. Let's count the letters in the original series again:

d (1), n (2), b (3), d (4), a (5), t (6), b (7), d (8), a (9), n (10), b (11), v (12). There are only 12 letters given, not 16. Let's assume there was a typo in my count, or in the question description if it mentioned 16 letters. The series `d _ n _ b _ d a _ t b _ d a n _ b v` with 6 blanks makes 18 positions.

Let's re-evaluate with 18 positions total, filling in Option 2 ('a t v n v t'):

d a n t b v d a n t b v d a n t b v

This does yield: `dantbv dantbv`. This pattern consists of the 6-letter block 'dantbv' repeated twice.

Let's check the positions of the blanks in the original series (18 positions total):

Position 2: `_` (should be 'a')
Position 4: `_` (should be 't')
Position 6: `_` (should be 'v')
Position 9: `_` (should be 'n')
Position 12: `_` (should be 'v')
Position 16: `_` (should be 't')

Let's see which letters from 'a t v n v t' fill which blanks:

• 1st blank (Pos 2) is filled by 'a' (1st letter of 'atvvnt')
• 2nd blank (Pos 4) is filled by 't' (2nd letter of 'atvvnt')
• 3rd blank (Pos 6) is filled by 'v' (3rd letter of 'atvvnt')
• 4th blank (Pos 9) is filled by 'n' (4th letter of 'atvvnt')
• 5th blank (Pos 12) is filled by 'v' (5th letter of 'atvvnt')
• 6th blank (Pos 16) is filled by 't' (6th letter of 'atvvnt')

This confirms that inserting 'a t v n v t' completes the series as 'dantbv' repeated twice.

Conclusion

By inserting the letters 'a t v n v t' into the blanks of the given letter series, we successfully form a clear repeating pattern 'dantbv'. Therefore, the combination of letters that completes the series is 'a t v n v t'.

The completed series is: d a n t b v d a n t b v

The letters filling the blanks are: a t v n v t

Revision Table: Letter Series Completion

Additional Information on Series Reasoning

Series completion questions are a core part of logical reasoning. They can involve various types of patterns beyond simple repeating blocks, such as:

• Alphabetical Order: Letters progressing or regressing in the alphabet (e.g., A, C, E, G...).
• Skipping Letters: Letters skipping a fixed number of letters (e.g., A, D, G, J... skipping 2 letters each time).
• Combination of Patterns: More complex rules involving position, vowel/consonant, or alternating sub-patterns.
• Number Series: Sequences of numbers following arithmetic, geometric, or other mathematical rules.
• Mixed Series: Combinations of letters and numbers.

Solving these questions often requires careful observation, trial and error with options, and systematic checking of potential rules.