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Refer to the following series and answer the question. (All numbers are single-digit numbers only. Counting to be done from left to right.) (Left) 2 4 9 6 7 1 4 6 3 9 5 2 4 8 6 1 3 2 7 6 2 5 8 1 (Right) How many such odd digits are there, each of the which is immediately preceded by an odd digit and immediately followed by an even digit?
One
Two
Four
Three
Three
Scan for sequences of (Odd, Odd, Even). The middle digit is the target, so look for two consecutive odds followed immediately by an even number.
Scan for sequences of (Odd, Odd, Even). The middle digit is the target, so look for two consecutive odds followed immediately by an even number.
Analyze the pattern requirements
We need triplets of (Odd, Odd, Even). Let the sequence be X, Y, Z where X = Odd, Y = Odd, and Z = Even. We are looking for the count of Y values.
Identify the triplets in the series
The series is: 2, 4, 9, 6, 7, 1, 4, 6, 3, 9, 5, 2, 4, 8, 6, 1, 3, 2, 7, 6, 2, 5, 8, 1. Analyzing consecutive segments: (9, 7, 1) - No, (7, 1, 4) - Yes (Odd, Odd, Even), (3, 9, 5) - No (9 is followed by odd 5), (9, 5, 2) - Yes (Odd, Odd, Even), (1, 3, 2) - Yes (Odd, Odd, Even).
Verify the count
The matching triplets are: 1) (7, 1, 4) where 1 is the middle digit, 2) (9, 5, 2) where 5 is the middle digit, 3) (1, 3, 2) where 3 is the middle digit. Total count is 3.
A: Only one found is incorrect as we identified three. B: Two is incorrect as we identified three. C: Four is incorrect as the sequence does not contain a fourth valid instance.
D is correct because there are exactly three occurrences (7,1,4), (9,5,2), and (1,3,2) that satisfy the condition of an odd digit being preceded by an odd and followed by an even digit.
When solving series problems, always mark the digits clearly to avoid skipping or double-counting, especially in long numerical strings.
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