2, 5, 11, 23, 47, 64, 191

Options

A. 2
B. 5
C. 23
D. 64

Explanation

To find the odd one out in the series 2, 5, 11, 23, 47, 64, 191, we will analyze the differences between consecutive terms and identify any patterns.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is:
\[ 2, 5, 11, 23, 47, 64, 191 \]

2. **Calculate the Differences**: We will calculate the differences between each pair of consecutive terms:
- \(5 - 2 = 3\)
- \(11 - 5 = 6\)
- \(23 - 11 = 12\)
- \(47 - 23 = 24\)
- \(64 - 47 = 17\)
- \(191 - 64 = 127\)

So, the differences are:
\[ 3, 6, 12, 24, 17, 127 \]

3. **Analyze the Differences**: Now, let's look for a pattern in the differences:
- The first four differences (3, 6, 12, 24) seem to follow a pattern of doubling:
- \(3 \times 2 = 6\)
- \(6 \times 2 = 12\)
- \(12 \times 2 = 24\)

4. **Identify the Anomaly**: The next difference is 17, which does not fit the doubling pattern. The expected difference after 24 should be:
- \(24 \times 2 = 48\)

5. **Calculate the Correct Term**: If we replace 64 with the correct term based on the expected difference:
- \(47 + 48 = 95\)

6. **Check the Last Difference**: Now, let's check the difference from the corrected term (95) to the next term (191):
- \(191 - 95 = 96\)
- This also does not fit the expected pattern since the next expected difference should be \(48 \times 2 = 96\).

7. **Conclusion**: The odd one out in the series is 64. The correct term should be 95.

### Final Answer:
The odd number in the series is **64**.

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