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Refer to the following number series and answer the question that follows. (All numbers are single-digit numbers only. Counting to be done from left to right only.) (Left) 3 5 4 3 6 7 8 9 9 6 6 3 3 7 8 8 1 7 5 3 (Right) How many such odd numbers are there, each of which is immediately preceded by an even number and also immediately followed by an odd number?
THREE
TWO
ONE
NONE
THREE
Scan for sequences of (Even)-(Odd)-(Odd) and mark the middle number immediately, ignoring everything else.
Scan for sequences of (Even)-(Odd)-(Odd) and mark the middle number immediately, ignoring everything else.
Analyze the series
The series is: 3, 5, 4, 3, 6, 7, 8, 9, 9, 6, 6, 3, 3, 7, 8, 8, 1, 7, 5, 3. The condition is: Even number, followed by an Odd number, followed by an Odd number.
Mapping and Verification
We look for Even(E) тЖТ Odd(O) тЖТ Odd(O) patterns: 1) 4, 3, 6 (No), 2) 6, 7, 8 (No), 3) 8, 9, 9 (Yes, 9 is preceded by 8 and followed by 9), 4) 6, 3, 3 (Yes, 3 is preceded by 6 and followed by 3), 5) 8, 1, 7 (Yes, 1 is preceded by 8 and followed by 7).
Counting valid instances
The triplets meeting the condition (Even, Odd, Odd) are: (8, 9, 9), (6, 3, 3), and (8, 1, 7). There are exactly 3 such instances.
B: Incorrect, as there are 3 instances not 2. C: Incorrect, as there is more than 1 instance. D: Incorrect, as there are definitely instances of the pattern.
A is correct because the sequence contains exactly three odd numbers that are immediately preceded by an even number and followed by an odd number: 9 (preceded by 8, followed by 9), 3 (preceded by 6, followed by 3), and 1 (preceded by 8, followed by 7).
In series problems with complex conditions, always rewrite the sequence as E/O labels to quickly visualize the pattern without getting distracted by the specific digit values.
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