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Refer to the following series: (Left) 3 5 2 8 1 7 4 9 6 3 2 5 8 4 1 9 6 2 7 3 5 4 8 2 (Right). How many such odd numbers are there each of which is immediately preceded by an even number and also immediately followed by an even number?
2
3
4
5
3
Scan for odd numbers first, then quickly verify the immediate left and right neighbors for parity (Even-Odd-Even).
Scan for odd numbers first, then quickly verify the immediate left and right neighbors for parity (Even-Odd-Even).
Analyze the series for triplets
The series is: 3, 5, 2, 8, 1, 7, 4, 9, 6, 3, 2, 5, 8, 4, 1, 9, 6, 2, 7, 3, 5, 4, 8, 2. We need to find triplets of the form (Even, Odd, Even).
Identify matches
Checking each odd number: 1 is preceded by 8 (E) and followed by 7 (O) - No. 7 is preceded by 1 (O) and followed by 4 (E) - No. 9 is preceded by 4 (E) and followed by 6 (E) - Yes (4,9,6). 3 is preceded by 6 (E) and followed by 2 (E) - Yes (6,3,2). 1 is preceded by 4 (E) and followed by 9 (O) - No. 9 is preceded by 1 (O) and followed by 6 (E) - No. 7 is preceded by 2 (E) and followed by 3 (O) - No. 3 is preceded by 7 (O) and followed by 5 (O) - No. 5 is preceded by 3 (O) and followed by 4 (E) - No.
Refined Triplets Search
Let's re-scan: 3 5 2 8 1 7 4 9 6 3 2 5 8 4 1 9 6 2 7 3 5 4 8 2. Triplets found: (4,9,6), (6,3,2), (4,1,9) - Wait, let's re-examine carefully: (8,1,7)-No, (4,9,6)-Yes, (6,3,2)-Yes, (4,1,9)-No, (6,2,7)-No, (2,7,3)-No, (8,4,1)-No, (4,5,4)-No. Wait, check 5: (2,5,8) - Yes. So the triplets are (4,9,6), (6,3,2), and (2,5,8).
A: Too low based on our triplet count. C: Too high as only 3 valid patterns exist. D: Incorrect as 5 valid patterns are not present in the sequence.
B is correct because the triplets (4,9,6), (6,3,2), and (2,5,8) satisfy the condition of an odd number being flanked by two even numbers.
When scanning sequences, underline the digits that meet the first condition (e.g., all odd numbers) to quickly check their neighbors without re-scanning the whole string.
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