3 5 10 12 17 23 24

Options

A. 5
B. 17
C. 24
D. None of these

Explanation

To identify the odd one out in the series 3, 5, 10, 12, 17, 23, 24, we will analyze the differences between the numbers and look for a pattern.

### Step-by-Step Solution:

1. **List the Series**:
The given series is:
\[ 3, 5, 10, 12, 17, 23, 24 \]

2. **Calculate Differences**:
We will find the differences between consecutive terms:
- \(5 - 3 = 2\)
- \(10 - 5 = 5\)
- \(12 - 10 = 2\)
- \(17 - 12 = 5\)
- \(23 - 17 = 6\)
- \(24 - 23 = 1\)

So, the differences are:
\[ 2, 5, 2, 5, 6, 1 \]

3. **Identify Patterns**:
The differences do not follow a consistent pattern. However, we can separate the series into two groups based on the observed differences:
- First group: \(3, 10, 17, 24\) (differences of 7)
- Second group: \(5, 12, 23\) (differences of 7 and then 11)

4. **Analyze the Second Group**:
In the second group, we notice:
- The difference between \(5\) and \(12\) is \(7\).
- The difference between \(12\) and \(23\) is \(11\).

This inconsistency suggests that \(12\) does not fit the pattern established by the other numbers.

5. **Find the Correct Middle Term**:
To find a consistent middle term, we can calculate the average of the two surrounding numbers:
\[ \text{Average of } 5 \text{ and } 23 = \frac{5 + 23}{2} = \frac{28}{2} = 14 \]
Thus, \(14\) should replace \(12\) to maintain a consistent pattern.

6. **Conclusion**:
The odd one out in the series is \(12\). Therefore, the correct answer is that \(12\) is the number that does not fit the pattern.