How many 5s are there in the following number sequence immediately preceded by an odd number, but NOT immediately followed by an odd number?
2564352956531649562421554967214755496425
2564352956531649562421554967214755496425
Show Hint
- Two
- Three
- Four
- Five
The Correct Option is D
Solution and Explanation
We need to scan the given sequence of digits and count the occurrences of the digit '5' that satisfy two specific conditions simultaneously: 1. The digit immediately before the '5' must be an odd number (1, 3, 5, 7, 9). 2. The digit immediately after the '5' must NOT be an odd number, which means it must be an even number (0, 2, 4, 6, 8) or the sequence must end there.
Step 2: Key Formula or Approach:
The approach is to systematically go through the sequence, identify every '5', and then check its preceding and succeeding digits against the given conditions. We will bold the instances that match the criteria.
Step 3: Detailed Explanation:
The sequence is: 2564352956531649562421554967214755496425
Let's examine each '5' in the sequence:
256: Preceded by 2 (Even). Does not satisfy the first condition.
352: Preceded by 3 (Odd). Followed by 2 (Even). This satisfies both conditions. (Count = 1)
956: Preceded by 9 (Odd). Followed by 6 (Even). This satisfies both conditions. (Count = 2)
653: Preceded by 6 (Even). Does not satisfy the first condition.
956: Preceded by 9 (Odd). Followed by 6 (Even). This satisfies both conditions. (Count = 3)
155: Preceded by 1 (Odd). Followed by 5 (Odd). Does not satisfy the second condition.
554: Preceded by 5 (Odd). Followed by 4 (Even). This satisfies both conditions. (Count = 4)
755: Preceded by 7 (Odd). Followed by 5 (Odd). Does not satisfy the second condition.
554: Preceded by 5 (Odd). Followed by 4 (Even). This satisfies both conditions. (Count = 5)
425: Preceded by 2 (Even). Does not satisfy the first condition.
Step 4: Final Answer:
By counting all the occurrences that meet the specified criteria, we find there are a total of five such 5s.
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