Refer to the following number series(Left) 4 9 8 5 1 6 4 5 9 6 5 3 4 9 6 2 9 4 8 5 1 1 8 4 1 5 7 (Right)
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.
निम्नलिखित संख्या श्रृंखला का संदर्भ लीजिए तथा दिए गए प्रश्न का उत्तर दीजिए। (सभी संख्याएँ केवल एकल-अंकीय हैं।) गिनती केवल बाएँ से दाएँ की जानी है।
(Left) 4 9 8 5 1 6 4 5 9 6 5 3 4 9 6 2 9 4 8 5 1 1 8 4 1 5 7 (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?
ऐसी कितनी विषम संख्याएँ हैं, जिनमें से प्रत्येक के ठीक पहले एक विषम संख्या है तथा ठीक बाद भी एक विषम संख्या है?
Detailed Solution & Logic
2
Step 1: Identify odd numbers
Odd numbers are: 1, 3, 5, 7, 9
The series is:
$4, 9, 8, 5, 1, 6, 4, 5, 9, 6, 5, 3, 4, 9, 6, 2, 9, 4, 8, 5, 1, 1, 8, 4, 1, 5, 7$
Step 2: Check each odd number (except first and last)
We check each odd number to see if both neighbors are odd:
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9 → neighbors 4 (even), 8 (even) → NO
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5 → neighbors 8 (even), 1 (odd) → NO
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1 → neighbors 5 (odd), 6 (even) → NO
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5 → neighbors 4 (even), 9 (odd) → NO
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9 → neighbors 5 (odd), 6 (even) → NO
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5 → neighbors 6 (even), 3 (odd) → NO
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3 → neighbors 5 (odd), 4 (even) → NO
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9 → neighbors 4 (even), 6 (even) → NO
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9 → neighbors 2 (even), 4 (even) → NO
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5 → neighbors 8 (even), 1 (odd) → NO
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1 → neighbors 5 (odd), 1 (odd) → YES ✅
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1 → neighbors 1 (odd), 8 (even) → NO
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1 → neighbors 4 (even), 5 (odd) → NO
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5 → neighbors 1 (odd), 7 (odd) → YES ✅
Step 3: Count
Numbers satisfying the condition: 1 and 5 → total 2 numbers
Answer: 2
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