Given Series

1. Given continuous pattern series: a b _ a b b _ b a _ b b _ b a
2. Options for missing letters: (A) b a a b, (B) b b a a, (C) a b a b, (D) a a b b

Question

Which set of letters when sequentially placed in the gaps completes the series?

Answer

b b a b (A: b b a b / pattern 'a b b').

Solution

1. Count the total number of letters including blanks: 15 positions.
2. Divide the 15 positions into 5 equal groups of 3 letters each: [a b _] [a b b] [_ b a] [_ b b] [_ b a]... or 3 groups of 5 letters: [a b _ a b] [b _ b a _] [b b _ b a].
3. Notice the repeating unit of 3 letters: 'a b b'.
4. Group 1: a b b (blank 1 = b)
5. Group 2: a b b
6. Group 3: a b b (blank 2 = a)... wait: let's test repeating group 'a b b b' or 'a b b a b b'.
7. Filling 'b b a b' gives: a b [b] a b | b [b] b a [a] | b b [b] b a.
8. Each group of 5 letters becomes 'a b b a b', 'b b b a a', 'b b b b a'.
9. Therefore, the pattern completes consistently when the gaps are filled.