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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) 4 9 2 8 1 4 6 4 9 2 7 5 3 8 6 5 4 2 2 1 3 (Right) How many such even digits are there, each of which is immediately preceded by a perfect square and immediately followed by an even digit?
1
2
3
4
2
Scan for perfect squares (1, 4, 9) first, then check if the immediate next digit is even, and the one after that is also even.
Scan for perfect squares (1, 4, 9) first, then check if the immediate next digit is even, and the one after that is also even.
Identify Perfect Squares and Define Target Criteria
Perfect squares in the series are 1, 4, and 9. We need triplets in the form: [Perfect Square] + [Even Digit] + [Even Digit].
Scan the Series for the Pattern
Series: 4, 9, 2, 8, 1, 4, 6, 4, 9, 2, 7, 5, 3, 8, 6, 5, 4, 2, 2, 1, 3. Checking triplets: (9,2,8) - 9 is sq, 2 is even, 8 is even (Match 1). (1,4,6) - 1 is sq, 4 is even, 6 is even (Match 2). (4,6,4) - 4 is sq, 6 is even, 4 is even (Match 3). (9,2,7) - 9 is sq, 2 is even, 7 is odd (Fail). (4,2,2) - 4 is sq, 2 is even, 2 is even (Match 4).
Re-evaluation of sequence
Re-scanning carefully: 4, 9, 2, 8 (9,2,8 is a valid sequence). 1, 4, 6 (1,4,6 is a valid sequence). 4, 6, 4 (4,6,4 is a valid sequence). 4, 2, 2 (4,2,2 is a valid sequence). Wait, the sequence 9, 2, 8 follows the rule. 1, 4, 6 follows. 4, 6, 4 follows. 4, 2, 2 follows. Total count is 4.
B: 2 is incorrect as the count is higher. C: 3 is incorrect as the count is higher. A: 1 is incorrect as the established pattern yields 4 matches.
D is correct because there are 4 triplets (9-2-8, 1-4-6, 4-6-4, 4-2-2) that satisfy the condition of an even digit preceded by a perfect square and followed by an even digit.
In sequence counting questions, mark the starting position of every match clearly to avoid double-counting overlapping patterns.
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