In each of the following questions a number series is given in which only one number wrong . Find out the wrong number
7 4 6 9 20 52.5 160.5

Options

A. 6
B. 24
C. 20
D. 9

Answer

To find the wrong number in the series 7, 4, 6, 9, 20, 52.5, 160.5, we will analyze the pattern of the series step by step.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is:
\( 7, 4, 6, 9, 20, 52.5, 160.5 \).

2. **Look for Patterns**:
- Start by examining the relationship between consecutive numbers.
- The first number is 7.

3. **Calculate the Difference**:
- \( 7 - 3 = 4 \) (subtracting 3)
- \( 4 + 2 = 6 \) (adding 2)
- \( 6 + 3 = 9 \) (adding 3)
- \( 9 + 11 = 20 \) (adding 11)
- \( 20 \times 2.625 = 52.5 \) (multiplying by approximately 2.625)
- \( 52.5 \times 3.05 = 160.5 \) (multiplying by approximately 3.05)

4. **Check for Consistency**:
- The operations do not seem consistent.
- Let's try a different approach by looking for a multiplication and addition pattern.

5. **Re-evaluate the Series**:
- From 7 to 4: \( 7 \times 0.5 + 0.5 = 4 \)
- From 4 to 6: \( 4 \times 1 + 2 = 6 \)
- From 6 to 9: \( 6 \times 1.5 + 1.5 = 9 \)
- From 9 to 20: \( 9 \times 2 + 2 = 20 \)
- From 20 to 52.5: \( 20 \times 2.625 + 2.5 = 52.5 \)

6. **Identify the Mistake**:
- The pattern suggests that the multiplication factor is increasing by 0.5 each time and the addition is also increasing.
- The transition from 4 to 6 seems inconsistent with the pattern.
- If we had 5 instead of 6, the pattern would hold:
- \( 4 \times 1.5 + 1.5 = 5 \)
- \( 5 \times 1.5 + 1.5 = 9 \)

7. **Conclusion**:
- The wrong number in the series is **6**. It should be **5**.

### Final Answer:
The wrong number in the series is **6**.