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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 2 9 1 3 2 9 4 1 6 8 5 4 3 7 6 4 2 8 1 3 5 (Right) How many such odd digits are there, each of the which is immediately preceded by an even digit and immediately followed by an even digit?
One
Four
Two
Three
Three
Scan for an odd digit and check if the digits immediately to its left and right are both even (divisible by 2).
Scan for an odd digit and check if the digits immediately to its left and right are both even (divisible by 2).
Define the Condition
We need to find an odd number (O) such that the sequence is Even - Odd - Even (E-O-E).
Series Analysis
The series is: 7(E), 2(E), 9(O), 1(O), 3(O), 2(E), 9(O), 4(E), 1(O), 6(E), 8(E), 5(O), 4(E), 3(O), 7(O), 6(E), 4(E), 2(E), 8(E), 1(O), 3(O), 5(O). Let's check for E-O-E patterns: 1) 2, 9, 4 (2 is E, 9 is O, 4 is E). 2) 4, 1, 6 (4 is E, 1 is O, 6 is E). 3) 4, 3, 7 (No, 7 is O, but 3 is O, not E). Checking further: 4) 8, 5, 4 (8 is E, 5 is O, 4 is E).
Final Verification
Triplets identified: 1) 2-9-4, 2) 4-1-6, 3) 8-5-4. All these contain an odd digit (9, 1, 5) surrounded by even digits (2,4; 4,6; 8,4). The count is 3.
A: Only one was found, which is incorrect as three exist. B: Four were found, which is incorrect as only three exist. C: Two were found, which is incorrect as three exist.
D is correct because there are exactly three instances of an odd digit preceded and followed by an even digit: 2-9-4, 4-1-6, and 8-5-4.
When counting elements in a series, use a pencil to underline the triplets as you find them to avoid double-counting or skipping elements.
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