In the series 5442673314884743581, the number of 4s that are completely divisible by the number on their right but not divisible by the number on their left is:
1
Analyzing the Number Series to Find Specific Digits
The given number series is: 5442673314884743581
We are asked to find the number of occurrences of the digit '4' that meet two specific conditions simultaneously:
- Condition 1: The '4' must be completely divisible by the digit immediately to its right.
- Condition 2: The '4' must NOT be divisible by the digit immediately to its left.
Let's examine each time the digit '4' appears in the series and check if both conditions are met. We need to look at the digit just before and just after each '4'.
| Occurrence of 4 | Left Neighbor | Right Neighbor | Is 4 divisible by Right Neighbor? (Condition 1) | Is 4 NOT divisible by Left Neighbor? (Condition 2) | Meets Both Conditions? |
|---|---|---|---|---|---|
| 1st 4 (between 5 and 4) | 5 | 4 | Yes, $\frac{4}{4} = 1$ (a whole number) | Yes, $\frac{4}{5}$ is not a whole number | Yes |
| 2nd 4 (between 4 and 2) | 4 | 2 | Yes, $\frac{4}{2} = 2$ (a whole number) | No, $\frac{4}{4} = 1$ (a whole number) | No |
| 3rd 4 (between 1 and 8) | 1 | 8 | No, $\frac{4}{8}$ is not a whole number | No, $\frac{4}{1} = 4$ (a whole number) | No |
| 4th 4 (between 8 and 7) | 8 | 7 | No, $\frac{4}{7}$ is not a whole number | Yes, $\frac{4}{8}$ is not a whole number | No |
| 5th 4 (between 7 and 3) | 7 | 3 | No, $\frac{4}{3}$ is not a whole number | Yes, $\frac{4}{7}$ is not a whole number | No |
As we can see from the table, only the first occurrence of '4' in the series satisfies both the condition of being divisible by its right neighbor (4) and not divisible by its left neighbor (5).
Result: Counting the Specific 4s
By systematically checking each '4' against the stated rules, we found that only one '4' in the series fits the description.
Therefore, the number of 4s that are completely divisible by the number on their right but not divisible by the number on their left is 1.
Revision Table: Understanding Number Series Questions
Let's quickly recap how to approach such number series analysis problems.
| Step | Action |
|---|---|
| 1 | Identify the target digit and the rules (conditions) it must satisfy based on its surrounding digits. |
| 2 | Scan through the given number series from start to end. |
| 3 | Every time the target digit is found, note its left and right neighbors. |
| 4 | Carefully check if the target digit satisfies all the given conditions based on its neighbors. |
| 5 | Keep a running count of the occurrences that satisfy ALL conditions. |
| 6 | The final count is your answer. |
Additional Information: Concepts in Number Series Analysis
Problems like this involve basic numerical reasoning and pattern identification. Here are some related concepts:
- Divisibility: A number A is divisible by number B if A divided by B gives an integer result with no remainder. For example, 6 is divisible by 3 because $6 \div 3 = 2$. 7 is not divisible by 3.
- Neighbors: In a linear series, the digits immediately adjacent to a specific digit are its neighbors. The digit to its left is the left neighbor, and the digit to its right is the right neighbor.
- Systematic Checking: It's important to go through the series methodically, checking each instance of the target digit to avoid missing any or miscounting.
- Reading Comprehension: Carefully read and understand the conditions given in the question. Pay attention to keywords like "completely divisible," "not divisible," "on their right," and "on their left."
Practicing different types of number series questions helps improve your ability to quickly identify patterns and apply conditions correctly.
Important Questions from Number Arrangement
Six friends A, B, C, D, E and F are sitting in two lines, facing the north. Three persons are sitting in each line. F is sitting in the middle. C is just behind B. D is to the immediate right of E. B is to the immediate left of F. Which three persons are sitting in the same line?
Refer to the following series and answer the question (all numbers are single digit numbers only).
(Left) 1 2 6 5 6 8 1 5 8 6 9 8 3 3 5 8 9 4 7 8 (Right)
How many such even digits are there, each of which is immediately preceded by an odd digit and also immediately followed by an odd digit?
Each of the digits in the number 9362145 is arranged in ascending order from left to right. What will be the sum of the digits which are second from the left and third from the right in the number thus formed?
If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 3842675, how many digits will appear more than once in the new number thus formed?
Refer to the following number and symbol series and answer the question that follows. Counting to be done from left to right only.
(Left) @ * $ 3 8 9 % + 7 > 6 # < % % ? 6 2 $ / 6 (Right)
How many such numbers are there, each of which is immediately preceded by a symbol and also immediately followed by a symbol?
