How many 6s are there in the following series of numbers which are preceded by 7 but not immediately followed by 9?
6 9 7 5 6 9 7 6 8 7 6 7 8 6 9 4 6 7 7 6 9 5 7 6 3

Options

A. one
B. Two
C. Three
D. Four

Explanation

To solve the problem, we need to identify how many times the number 6 appears in the series, specifically when it is preceded by the number 7 and not immediately followed by the number 9. Let's go through the series step by step.

### Step-by-Step Solution:

1. **Identify the Series**:
The series of numbers is:
6, 9, 7, 5, 6, 9, 7, 6, 8, 7, 6, 7, 8, 6, 9, 4, 6, 7, 7, 6, 9, 5, 7, 6, 3.

2. **Locate the Occurrences of 6**:
We will scan through the series to find each occurrence of the number 6.

3. **Check Conditions for Each 6**:
- For each 6 found, check if it is preceded by a 7 and not immediately followed by a 9.

4. **Examine Each 6**:
- **1st 6**: (Position 1) - No 7 before it. **(Not counted)**
- **2nd 6**: (Position 4) - Preceded by 5. **(Not counted)**
- **3rd 6**: (Position 7) - Preceded by 7 and followed by 8. **(Counted)**
- **4th 6**: (Position 10) - Preceded by 7 and followed by 7. **(Counted)**
- **5th 6**: (Position 14) - Preceded by 8. **(Not counted)**
- **6th 6**: (Position 16) - Preceded by 9. **(Not counted)**
- **7th 6**: (Position 17) - Preceded by 4. **(Not counted)**
- **8th 6**: (Position 19) - Preceded by 7 and followed by 9. **(Not counted)**
- **9th 6**: (Position 21) - Preceded by 7 and followed by 5. **(Counted)**
- **10th 6**: (Position 22) - Preceded by 5. **(Not counted)**
- **11th 6**: (Position 23) - Preceded by 7 and followed by 3. **(Counted)**

5. **Count the Valid 6s**:
- The valid occurrences of 6 that meet the criteria are:
- 6 (Position 7)
- 6 (Position 10)
- 6 (Position 22)
- 6 (Position 23)
- Total valid 6s = 4.

### Final Answer:
There are **4** occurrences of the number 6 that are preceded by 7 and not immediately followed by 9.

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