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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 9 2 6 1 2 6 4 8 2 7 5 9 8 6 5 4 2 2 1 3 (Right) How many such even digits are there, each of the which is immediately preceded by a perfect square and immediately followed by an even digit? (NOTE: 1 is also a perfect square)
Three
Five
Four
Two
Five
Identify all perfect squares (1, 4, 9) first, then scan triplets where a perfect square is followed by an even digit, which is then followed by another even digit.
Identify all perfect squares (1, 4, 9) first, then scan triplets where a perfect square is followed by an even digit, which is then followed by another even digit.
List the sequence and identify perfect squares
The sequence is 7, 9, 2, 6, 1, 2, 6, 4, 8, 2, 7, 5, 9, 8, 6, 5, 4, 2, 2, 1, 3. Perfect squares in this set are 1, 4, and 9.
Search for the required triplet pattern
We need the pattern: (Perfect Square) тЖТ (Even Digit) тЖТ (Even Digit). Let's scan: (9, 2, 6) тЖТ 9 is square, 2 is even, 6 is even (Match 1). (1, 2, 6) тЖТ 1 is square, 2 is even, 6 is even (Match 2). (4, 8, 2) тЖТ 4 is square, 8 is even, 2 is even (Match 3). (9, 8, 6) тЖТ 9 is square, 8 is even, 6 is even (Match 4). (4, 2, 2) тЖТ 4 is square, 2 is even, 2 is even (Match 5).
Final count verification
Total occurrences of the pattern (Perfect Square, Even, Even) are 5. The identified triplets are (9,2,6), (1,2,6), (4,8,2), (9,8,6), and (4,2,2).
A: Represents a count of 3, ignoring valid triplets found at the end of the series. C: Represents a count of 4, missing one instance found in the middle of the string. D: Represents a count of 2, failing to identify the majority of valid patterns.
B is correct because there are exactly five instances of an even digit preceded by a perfect square and followed by an even digit: (9,2,6), (1,2,6), (4,8,2), (9,8,6), and (4,2,2).
In alphanumeric series questions involving 'preceded by' and 'followed by', always underline the target condition pattern first to avoid losing track during scanning.
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