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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 even digits are there, each of which is immediately preceded by an odd digit and also immediately followed by an odd digit?
2
4
3
5
5
Identify the triplet structure (Odd-Even-Odd) by scanning the series: look for an even digit (2, 4, 6, 8) and check if the digits immediately to its left and right are both odd (1, 3, 5, 7, 9).
Identify the triplet structure (Odd-Even-Odd) by scanning the series: look for an even digit (2, 4, 6, 8) and check if the digits immediately to its left and right are both odd (1, 3, 5, 7, 9).
Define the Condition
We need to find an even digit (2, 4, 6, 8) that is immediately preceded by an odd digit (1, 3, 5, 7, 9) and immediately followed by an odd digit (1, 3, 5, 7, 9).
Scan the Series
Series: 5, 1, 6, 6, 2, 4, 9, 3, 5, 3, 7, 1, 8, 5, 2, 7, 8, 1, 8, 4, 5, 1, 5, 7, 6, 9, 2, 9. Checking every even digit: (1) 6: 1-6-6 (No), (2) 6: 6-6-2 (No), (3) 2: 6-2-4 (No), (4) 4: 2-4-9 (Yes), (5) 8: 1-8-5 (Yes), (6) 2: 5-2-7 (Yes), (7) 8: 7-8-1 (Yes), (8) 8: 1-8-4 (No), (9) 4: 8-4-5 (No), (10) 6: 7-6-9 (Yes), (11) 2: 9-2-9 (Yes).
Count Verified Triplets
The triplets are: (2, 4, 9), (1, 8, 5), (5, 2, 7), (7, 8, 1), (7, 6, 9), (9, 2, 9). Re-evaluating: 2-4-9 (Yes), 1-8-5 (Yes), 5-2-7 (Yes), 7-8-1 (Yes), 7-6-9 (Yes), 9-2-9 (Yes). Total count is 6.
A: 4 is incorrect, B: 5 is incorrect, C: 7 is incorrect. The verified count is 6, which matches option D.
D is correct because there are exactly 6 even digits in the sequence that are surrounded by odd digits on both sides: 2-4-9, 1-8-5, 5-2-7, 7-8-1, 7-6-9, and 9-2-9.
In series scanning questions, always break the sequence into small overlapping triplets (3 digits each) to ensure no digits are missed or double-counted.
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