Directions: In each question, four numbers are given out of which three are alike in same manner while one is different. Choose the odd one out.

Options

A. 7
B. 15
C. 31
D. 57

Explanation

To solve the problem of identifying the odd number out from the given set of numbers (7, 15, 31, 57), we will analyze the numbers based on a specific mathematical pattern.

### Step-by-Step Solution:

1. **List the Given Numbers**:
The numbers provided are 7, 15, 31, and 57.

2. **Identify a Pattern**:
We will check if these numbers can be expressed in a similar mathematical form. A common pattern to check is if they can be expressed as \(2^n - 1\).

3. **Calculate for Each Number**:
- For 7:
\[ 2^3 - 1 = 8 - 1 = 7 \]
- For 15:
\[ 2^4 - 1 = 16 - 1 = 15 \]
- For 31:
\[ 2^5 - 1 = 32 - 1 = 31 \]
- For 57:
\[ 2^6 - 1 = 64 - 1 = 63 \quad (\text{not equal to } 57) \]

4. **Compare the Results**:
From the calculations:
- 7 can be expressed as \(2^3 - 1\)
- 15 can be expressed as \(2^4 - 1\)
- 31 can be expressed as \(2^5 - 1\)
- 57 cannot be expressed in the same form, as it does not equal \(2^n - 1\) for any integer \(n\).

5. **Identify the Odd One Out**:
Since 57 does not fit the pattern of being expressed as \(2^n - 1\), it is the odd one out.

### Conclusion:
The odd number out is **57**.

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