Directions: What will come in the place of question mark in following number series?
8,?,4,6,12,30

Options

A. 15
B. 8
C. 4
D. 2

Answer

To solve the number series: 8, ?, 4, 6, 12, 30, we need to identify the pattern in the series.

### Step-by-step Solution:

1. **Identify the Known Numbers**: The series starts with 8, followed by a question mark (?), then 4, 6, 12, and 30.

2. **Analyze the Series**: Let's look at the numbers we have: 4, 6, 12, and 30. We need to find a relationship between them.

3. **Observe the Pattern**:
- From 4 to 6:
- \(4 \times 1.5 = 6\) (or \(4 + 2 = 6\))
- From 6 to 12:
- \(6 \times 2 = 12\) (or \(6 + 6 = 12\))
- From 12 to 30:
- \(12 \times 2.5 = 30\) (or \(12 + 18 = 30\))

4. **Determine the Missing Number**:
- Now, we need to find the number that comes before 4 (the question mark).
- If we assume the pattern continues, we can see that the multiplication factor is increasing by 0.5 each time (1.5, 2, 2.5).
- To find the number before 4, we can reverse the operation:
- If we take 4 and divide it by 1.5 (the factor used to get to 6), we can find the previous number:
- \(4 \div 1.5 = \frac{4}{1.5} = \frac{8}{3} \approx 2.67\)

5. **Check the Pattern**:
- If we take the number we found (approximately 2.67) and check if it fits into the series:
- From 2.67 to 4:
- \(2.67 \times 1.5 \approx 4\)
- This shows that the pattern holds.

6. **Conclusion**: The number that replaces the question mark is approximately 2.67.

### Final Answer:
The number that comes in place of the question mark is approximately **2.67**.