In the series given below, how many 8’s are there each of which ...
Understanding the Problem
In the given series, we need to identify the occurrences of the number 8 that are exactly divisible by both the numbers immediately before and after them.
Series Breakdown
The series is:
2, 8, 4, 3, 8, 5, 4, 8, 2, 6, 7, 8, 4, 6, 2, 8, 4, 1, 7
Identifying Relevant 8's
We will analyze each occurrence of the number 8:
- First 8 (2, 8, 4)
- Preceding number: 2
- Succeeding number: 4
- 8 is divisible by 2 (8 ÷ 2 = 4) and by 4 (8 ÷ 4 = 2).
- Valid 8
- Second 8 (3, 8, 5)
- Preceding number: 3
- Succeeding number: 5
- 8 is not divisible by 3 (8 ÷ 3 = 2.67) and not divisible by 5 (8 ÷ 5 = 1.6).
- Invalid 8
- Third 8 (4, 8, 2)
- Preceding number: 4
- Succeeding number: 2
- 8 is divisible by 4 (8 ÷ 4 = 2) and by 2 (8 ÷ 2 = 4).
- Valid 8
- Fourth 8 (6, 8, 4)
- Preceding number: 6
- Succeeding number: 4
- 8 is not divisible by 6 (8 ÷ 6 = 1.33) and by 4 (8 ÷ 4 = 2).
- Invalid 8
- Fifth 8 (2, 8, 4)
- Preceding number: 2
- Succeeding number: 4
- 8 is divisible by 2 and by 4.
- Valid 8
- Sixth 8 (4, 8, 1)
- Preceding number: 4
- Succeeding number: 1
- 8 is divisible by 4 and by 1.
- Valid 8
Conclusion
In total, we have three valid occurrences of 8 that meet the criteria. Therefore, the answer is 3.