125, 127,130,135,142,153,165

Options

A. 130
B. 142
C. 153
D. 165

Answer

To find the odd number in the series 125, 127, 130, 135, 142, 153, and 165, we will analyze the differences between the consecutive terms and check if they follow a specific pattern.

### Step-by-Step Solution:

1. **List the Series**:
We start with the given series:
\[ 125, 127, 130, 135, 142, 153, 165 \]

2. **Calculate the Differences**:
We will find the difference between each consecutive pair of numbers:
- \(127 - 125 = 2\)
- \(130 - 127 = 3\)
- \(135 - 130 = 5\)
- \(142 - 135 = 7\)
- \(153 - 142 = 11\)
- \(165 - 153 = 12\)

So, the differences are:
\[ 2, 3, 5, 7, 11, 12 \]

3. **Identify the Pattern**:
Now we check if these differences are prime numbers:
- \(2\) is prime
- \(3\) is prime
- \(5\) is prime
- \(7\) is prime
- \(11\) is prime
- \(12\) is **not** prime

4. **Determine the Odd Number**:
Since all the differences except for the last one (which is \(12\)) are prime numbers, we can conclude that \(165\) is the odd number in the series because it does not follow the established pattern of prime differences.

5. **Final Conclusion**:
Therefore, the odd number in the series is:
\[ \text{Odd number: } 165 \]