15, 13, 22, 147, 196, 925, 1046

Options

A. 13
B. 1046
C. 15
D. 925

Explanation

To find the odd one out in the series: 15, 13, 22, 147, 196, 925, 1046, we will analyze the differences between consecutive numbers and identify any patterns.

### Step-by-Step Solution:

1. **Identify the numbers in the series**:
- The series is: 15, 13, 22, 147, 196, 925, 1046.

2. **Calculate the differences between consecutive numbers**:
- Difference between 15 and 13:
\[ 13 - 15 = -2 \]
- Difference between 13 and 22:
\[ 22 - 13 = 9 \]
- Difference between 22 and 147:
\[ 147 - 22 = 125 \]
- Difference between 147 and 196:
\[ 196 - 147 = 49 \]
- Difference between 196 and 925:
\[ 925 - 196 = 729 \]
- Difference between 925 and 1046:
\[ 1046 - 925 = 121 \]

3. **List the differences**:
- The differences are: -2, 9, 125, 49, 729, 121.

4. **Identify the pattern in the differences**:
- The differences can be analyzed as follows:
- \(9 = 3^2\)
- \(125 = 5^3\)
- \(49 = 7^2\)
- \(729 = 9^3\)
- \(121 = 11^2\)

5. **Recognize the alternating pattern**:
- The pattern alternates between squares of odd numbers and cubes of odd numbers:
- Square of 3, Cube of 5, Square of 7, Cube of 9, Square of 11.
- The first difference (-2) does not fit this pattern.

6. **Determine the correct number**:
- Instead of -2, we should have a difference of 1 (which is \(1^2\)).
- Therefore, we need to replace 15 with a number that gives a difference of 1 from 13:
\[ 13 - 1 = 12 \]

7. **Conclusion**:
- The odd one out in the series is **15**. If we replace 15 with 12, the series will follow the identified pattern.

### Final Answer:
The odd one out in the series is **15**.