A pattern formed by two characters a and b is repeated more than once in the following string : x b x a x a x x a x a x b a b What is x x in the 7th and 8th positions from the left in the above string?

This question is a classic example of a Continuous Pattern Series found in logical reasoning aptitude tests like the UPSC CSAT. The objective is to determine a logically repeating sequence by observing the given characters and placeholders (denoted here by 'x').

Why Option D is correct: First, we count the total number of positions in the given string: x b x a x a x x a x a x b a b The total length is 15 characters. To find a repeating pattern, we factorize the total length. A 15-character sequence typically breaks into uniform blocks of 3 or 5. Let us divide the series into three equal groups of 5 characters each:

• Group 1 (Positions 1 to 5): x b x a x
• Group 2 (Positions 6 to 10): a x x a x
• Group 3 (Positions 11 to 15): a x b a b

By aligning these blocks and comparing corresponding positions, we deduce the underlying sequence:

• 1st position: x, a, a → Must be a
• 2nd position: b, x, x → Must be b
• 3rd position: x, x, b → Must be b
• 4th position: a, a, a → Confirmed as a
• 5th position: x, x, b → Must be b

The universally repeated pattern is a b b a b. The question asks for the 'x x' values at the 7th and 8th positions from the left. These correspond to the 2nd and 3rd characters of Group 2. Since the 2nd and 3rd characters in the fundamental pattern are both 'b', the 7th and 8th positions must be bb.

Why the other options are incorrect:

• Option A (aa): Incorrect because assigning 'a' to the 7th and 8th positions contradicts the confirmed pattern where the 2nd and 3rd letters of each block must be 'b'.
• Option B (ab): Incorrect. Substituting 'a' into the 7th position violates the pattern established unequivocally by the 'b' sitting in the 2nd position of the first block.
• Option C (ba): Incorrect. Placing 'a' in the 8th position contradicts the 13th character of the string, which firmly establishes that the 3rd letter of every block must be 'b'.

Takeaway: When solving continuous sequence puzzles, immediately count the total characters (including blanks) and divide them into equal-length groupings based on the total's factors (e.g., 15 elements easily split into 3 blocks of 5). Align the groups vertically to swiftly reveal the hidden pattern.