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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) 7 3 2 5 1 4 6 8 3 4 9 7 5 4 2 6 1 7 9 (Right) How many such digits are there, each of which is immediately preceded by an even digit and immediately followed by an odd digit?
Four
Two
Five
Three
Five
Scan the series for even numbers (2, 4, 6, 8) and check if the digits immediately flanking them are (Even, X, Odd).
Scan the series for even numbers (2, 4, 6, 8) and check if the digits immediately flanking them are (Even, X, Odd).
Define the target pattern
We need to find a pattern: [Even Digit] тЖТ [Any Digit] тЖТ [Odd Digit]. Since the question asks for a digit 'preceded by an even digit and followed by an odd digit', we look for triplets (E, X, O) where X is the middle digit.
Scan the sequence
The sequence is: 7 3 2 5 1 4 6 8 3 4 9 7 5 4 2 6 1 7 9. Checking triplets (E, X, O): 1) (2, 5, 1) - Valid. 2) (4, 6, 8) - Invalid (8 is even). 3) (6, 8, 3) - Valid. 4) (4, 9, 7) - Invalid (9 is odd, not even). 5) (4, 2, 6) - Invalid (6 is even). 6) (2, 6, 1) - Valid. 7) (8, 3, 4) - Invalid. Let us re-scan carefully: (2,5,1), (6,8,3), (4,9,7) NO (preceded by 4 even, followed by 9 odd - wait), let's look again: 7, 3, 2, 5, 1, 4, 6, 8, 3, 4, 9, 7, 5, 4, 2, 6, 1, 7, 9. Pairs: (2,5,1), (6,8,3), (8,3,4)NO, (4,9,7), (2,6,1), (6,1,7).
Final verification of valid triplets
Valid triplets (Even, X, Odd) are: 1) (2, 5, 1), 2) (6, 8, 3), 3) (4, 9, 7), 4) (2, 6, 1), 5) (6, 1, 7). Total count is 5.
A: Four is incorrect as there are 5 occurrences. B: Two is incorrect as it undercounts the valid triplets. D: Three is incorrect as it fails to identify all qualifying sequences.
C is correct because a manual scan of the series confirms five triplets follow the Even-Digit-Odd structure: (2,5,1), (6,8,3), (4,9,7), (2,6,1), and (6,1,7).
When counting specific triplets in a long series, write the series clearly with space between digits and mark every valid occurrence to avoid double-counting or skipping.
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