How many 5s are there in the following number series which are immediately followed by 3 but not immediately preceded by 7?
2 1 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 2 5 7 3 9

Options

A. One
B. Two
C. Three
D. four

Explanation

To solve the problem of counting how many 5s are immediately followed by 3 but not immediately preceded by 7 in the given number series, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Number Series**:
The series given is:
2, 1, 5, 3, 2, 5, 3, 8, 5, 5, 6, 8, 7, 3, 3, 5, 7, 7, 5, 3, 6, 5, 3, 2, 5, 7, 3, 9

2. **Scan for 5s Followed by 3**:
We need to find instances of the number 5 that are immediately followed by the number 3.

- The occurrences of 5 followed by 3 in the series are:
- 5 (at index 2) followed by 3 (at index 3)
- 5 (at index 5) followed by 3 (at index 6)
- 5 (at index 15) followed by 3 (at index 16)
- 5 (at index 20) followed by 3 (at index 21)

3. **Check Preceding Numbers**:
Now, we need to check if any of these 5s are preceded by 7.

- The first occurrence (5 at index 2) is preceded by 1 (not 7) → valid
- The second occurrence (5 at index 5) is preceded by 2 (not 7) → valid
- The third occurrence (5 at index 15) is preceded by 7 (not valid)
- The fourth occurrence (5 at index 20) is preceded by 7 (not valid)

4. **Count Valid Instances**:
From the valid instances, we have:
- 5 at index 2 (valid)
- 5 at index 5 (valid)

Therefore, the total count of 5s that are immediately followed by 3 and not immediately preceded by 7 is **2**.

5. **Final Answer**:
The answer is 2.