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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 a perfect square and immediately followed by an even digit? (Note: 1 will be considered as a perfect square.)
0
2
3
1
2
Scan the series for triplets (Perfect Square, Even, Even) from left to right, keeping in mind that 1, 4, and 9 are the only single-digit perfect squares.
Scan the series for triplets (Perfect Square, Even, Even) from left to right, keeping in mind that 1, 4, and 9 are the only single-digit perfect squares.
Identify Target Pattern
We need to find an even digit (E) that is immediately preceded by a perfect square (S) and immediately followed by an even digit (E). The pattern is (S, E, E). Perfect squares are 1, 4, and 9.
Analyze the Series
Series: 7, 2, 5, 5, 2, 1, 9, 2, 4, 1, 2, 2, 6, 9, 5, 5, 5, 3, 8, 5, 5, 3, 1, 1, 6, 3, 3. Checking triplets: (1, 9, 2) - No, (9, 2, 4) - Yes (9 is square, 2 is even, 4 is even). (4, 1, 2) - No (1 is not even). (1, 2, 2) - Yes (1 is square, 2 is even, 2 is even). (2, 2, 6) - No. (6, 9, 5) - No. (3, 8, 5) - No. Only two triplets fit: (9, 2, 4) and (1, 2, 2).
A: Represents an undercount; C: Represents an overcount; D: Represents an overcount.
B is correct because the series contains exactly two even digits that satisfy the condition: the 2 in (9, 2, 4) and the 2 in (1, 2, 2).
Always verify if 1 is included in the definition of a perfect square in the question, as it is often a common trap in competitive exams.
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