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Refer to the given series and answer the question that follows (all numbers are single-digit numbers only, and all counting is to be done from left to right).
How many such odd digits are there, each of which is immediately preceded by an odd digit and also immediately followed by an odd digit?
4
2
3
1
3
Scan the series for triplets of odd digits (1, 3, 5, 7, 9). Ignore all even digits (2, 4, 6, 8) and look for three consecutive odd numbers.
Scan the series for triplets of odd digits (1, 3, 5, 7, 9). Ignore all even digits (2, 4, 6, 8) and look for three consecutive odd numbers.
Analyze the series for odd-digit triplets
The given series is: 9, 7, 4, 5, 1, 8, 2, 7, 5, 1, 3, 4, 2, 3, 7, 4, 9, 5, 2, 7, 5, 6, 9, 2, 8, 5, 4, 1, 9, 3. We need to find odd digits immediately preceded and followed by an odd digit, which means we are looking for patterns of (Odd, Odd, Odd).
Identify sequences of three consecutive odd digits
Let us check the groups: (9, 7, 4 - no), (7, 4, 5 - no), (5, 1, 8 - no), (1, 8, 2 - no), (2, 7, 5 - no), (7, 5, 1 - YES), (5, 1, 3 - YES), (1, 3, 4 - no), (3, 4, 2 - no), (2, 3, 7 - no), (3, 7, 4 - no), (7, 4, 9 - no), (4, 9, 5 - no), (9, 5, 2 - no), (5, 2, 7 - no), (2, 7, 5 - no), (7, 5, 6 - no), (5, 6, 9 - no), (6, 9, 2 - no), (9, 2, 8 - no), (2, 8, 5 - no), (8, 5, 4 - no), (5, 4, 1 - no), (4, 1, 9 - no), (1, 9, 3 - YES).
Count the identified occurrences
The sequences identified are: 1) (7, 5, 1) where 5 is the middle digit, 2) (5, 1, 3) where 1 is the middle digit, 3) (1, 9, 3) where 9 is the middle digit. Thus, there are 3 such occurrences.
A: Represents 2, which is incorrect. B: Represents 4, which is incorrect. D: Represents 5, which is incorrect.
C is correct because there are exactly 3 instances where an odd digit is flanked by odd digits: (7, 5, 1), (5, 1, 3), and (1, 9, 3).
In such series questions, always write down the parity (O for odd, E for even) below each digit to visually highlight O-O-O patterns quickly.
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