In the given series, how many 8s are there that are not divisible by the number to its left but completely divisible by the number to its right.
1
Analyzing Number Series for Specific Conditions
The question asks us to analyze a given number series and count the occurrences of the digit '8' that satisfy two specific conditions:
- The number immediately to the left of the '8' does not completely divide the '8'.
- The number immediately to the right of the '8' completely divides the '8'.
Let's look at the series provided: 5 6 3 2 4 8 8 8 9 2 6 6 5 8 8 3 4 3
We need to identify each '8' in the series and examine its neighbours (the number to its left and the number to its right).
Step-by-Step Analysis of Each '8'
Let's go through the series and identify each instance of '8' and its surrounding numbers to check if both conditions are met.
| '8' Instance | Number to the Left | Number to the Right | Condition 1: Is 8 divisible by Left? | Condition 2: Is 8 divisible by Right? | Both Conditions Met? |
|---|---|---|---|---|---|
| 1st '8' (after 4) | 4 | 8 | Yes ($\frac{8}{4} = 2$). Condition 1 is NOT met. | Yes ($\frac{8}{8} = 1$). Condition 2 is met. | No |
| 2nd '8' (after 8) | 8 | 8 | Yes ($\frac{8}{8} = 1$). Condition 1 is NOT met. | Yes ($\frac{8}{8} = 1$). Condition 2 is met. | No |
| 3rd '8' (after 8) | 8 | 9 | Yes ($\frac{8}{8} = 1$). Condition 1 is NOT met. | No ($\frac{8}{9}$ is not an integer). Condition 2 is NOT met. | No |
| 4th '8' (after 5) | 5 | 8 | No ($\frac{8}{5}$ is not an integer). Condition 1 is met. | Yes ($\frac{8}{8} = 1$). Condition 2 is met. | Yes |
| 5th '8' (after 8) | 8 | 3 | Yes ($\frac{8}{8} = 1$). Condition 1 is NOT met. | No ($\frac{8}{3}$ is not an integer). Condition 2 is NOT met. | No |
Based on the analysis, only one instance of '8' in the series satisfies both conditions:
- The '8' that has '5' to its left and '8' to its right (part of the sequence ...5 8 8...). Here, 8 is not divisible by 5, but 8 is divisible by 8.
Conclusion on Counting 8s
We found that only 1 instance of '8' in the given series meets the criteria of not being divisible by the number on its left but being divisible by the number on its right.
Revision Table: Checking the Conditions for 8s in Series
| Location in Series | Number Left | The '8' | Number Right | 8 Not Divisible by Left? | 8 Divisible by Right? | Counted? |
|---|---|---|---|---|---|---|
| ...4 8 8... | 4 | 8 | 8 | No ($\frac{8}{4}=2$) | Yes ($\frac{8}{8}=1$) | No |
| ...8 8 8... | 8 | 8 | 8 | No ($\frac{8}{8}=1$) | Yes ($\frac{8}{8}=1$) | No |
| ...8 8 9... | 8 | 8 | 9 | No ($\frac{8}{8}=1$) | No ($\frac{8}{9}$) | No |
| ...5 8 8... | 5 | 8 | 8 | Yes ($\frac{8}{5}$) | Yes ($\frac{8}{8}=1$) | Yes |
| ...8 8 3... | 8 | 8 | 3 | No ($\frac{8}{8}=1$) | No ($\frac{8}{3}$) | No |
Additional Information: Understanding Divisibility in Number Series
This problem is a common type found in logical reasoning and quantitative aptitude sections of exams. It tests your ability to follow specific rules and apply them systematically to a sequence of numbers.
- Divisibility: A number 'a' is completely divisible by a number 'b' if dividing 'a' by 'b' results in an integer with no remainder. For example, 8 is divisible by 4 because $8 \div 4 = 2$. 8 is not divisible by 5 because $8 \div 5 = 1.6$.
- Series Analysis: Problems like this require careful observation and a step-by-step approach. It's helpful to list out the instances you are looking for (in this case, the digit '8') and then apply the conditions to each instance one by one.
- Avoiding Errors: The most common mistake is misinterpreting the conditions or incorrectly performing the divisibility check. Ensure you check BOTH conditions for each target number ('8' in this case) before deciding if it should be counted.
These types of questions help improve attention to detail and logical thinking skills.
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