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Refer to the given 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) 4 2 8 3 7 4 7 1 6 1 3 1 3 9 3 6 6 5 6 7 4 8 4 9 1 9 3 (Right) How many such odd numbers are there, each of which is immediately preceded by an odd number and also immediately followed by an odd number?
7
5
6
8 Question ID : 441009780423 Option 1 ID : 4410093075696 Option 2 ID : 4410093075697 Option 3 ID : 4410093075695 Option 4 ID : 4410093075698 Status : Answered Chosen Option : C
6
Scan for triplets of odd numbers (O-O-O) by ignoring all even numbers entirely in your visual sweep.
Scan for triplets of odd numbers (O-O-O) by ignoring all even numbers entirely in your visual sweep.
Filter the sequence for Odd numbers
The original series is: 4 2 8 3 7 4 7 1 6 1 3 1 3 9 3 6 6 5 6 7 4 8 4 9 1 9 3. Extracting only the odd numbers in order: 3, 7, 7, 1, 1, 3, 1, 3, 9, 3, 5, 7, 9, 1, 9, 3.
Identify triplets (Odd-Odd-Odd)
We look for groups of three consecutive odd numbers in the original series: (3, 7, 1) is invalid because of the 4/6 interruption. Scanning the original string for O-O-O: 1) 3-7-?, 2) 7-1-?, 3) 1-3-1, 4) 3-1-3, 5) 1-3-9, 6) 3-9-3, 7) 9-1-9, 8) 1-9-3. Let us re-examine precisely: [3, 7, 4(X)], [7, 1, 6(X)], [1, 3, 1] (Found: 1), [3, 1, 3] (Found: 2), [1, 3, 9] (Found: 3), [3, 9, 3] (Found: 4), [5, 6(X)], [9, 1, 9] (Found: 5), [1, 9, 3] (Found: 6).
A: 7 is incorrect as only 6 sequences meet the criteria. B: 5 is incorrect because it misses the 6th sequence. D: 8 is incorrect as it overcounts the overlaps.
C is correct because a manual scan of the series confirms exactly 6 occurrences of an odd number flanked by two other odd numbers (131, 313, 139, 393, 919, 193).
When counting triplets, write the sequence out and underline the patterns to avoid skipping overlapping numbers like the middle number in 1-3-9.
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