525, 310, 186, 123, 97, 89, 90

Options

A. 90
B. 525
C. 186
D. 89

Explanation

To find the odd one out in the series: 525, 310, 186, 123, 97, 89, 90, we will analyze the differences and patterns in the numbers.

### Step 1: Identify the differences between consecutive numbers
1. **Difference between 525 and 310**:
\[ 525 - 310 = 215 \]
2. **Difference between 310 and 186**:
\[ 310 - 186 = 124 \]
3. **Difference between 186 and 123**:
\[ 186 - 123 = 63 \]
4. **Difference between 123 and 97**:
\[ 123 - 97 = 26 \]
5. **Difference between 97 and 89**:
\[ 97 - 89 = 8 \]
6. **Difference between 89 and 90**:
\[ 90 - 89 = 1 \]

### Step 2: Analyze the pattern in the differences
The differences we calculated are:
- 215
- 124
- 63
- 26
- 8
- 1

### Step 3: Check for a pattern in the differences
The differences do not seem to follow a consistent arithmetic or geometric pattern. However, we can check if the numbers are related to perfect cubes.

### Step 4: Identify if numbers are related to cubes
1. **Cube of 6**:
\[ 6^3 = 216 \quad \text{(216 - 1 = 215)} \]
2. **Cube of 5**:
\[ 5^3 = 125 \quad \text{(125 - 1 = 124)} \]
3. **Cube of 4**:
\[ 4^3 = 64 \quad \text{(64 - 1 = 63)} \]
4. **Cube of 3**:
\[ 3^3 = 27 \quad \text{(27 - 1 = 26)} \]
5. **Cube of 2**:
\[ 2^3 = 8 \quad \text{(8 - 1 = 7)} \]
6. **Cube of 1**:
\[ 1^3 = 1 \quad \text{(1 - 1 = 0)} \]

### Step 5: Identify the missing number
Following the pattern of cubes:
- The next number after 26 should be \( 26 - 7 = 19 \).
- The next number after 19 should be \( 19 - 0 = 19 \).

### Step 6: Compare with the given series
The series should have been:
- 525, 310, 186, 123, 97, 90, 90

However, the series has 89 instead of 90.

### Conclusion
The odd one out in the series is **89**. The correct number should be **90**.