In each of the following questions, four numbers are given. Out of these three are alike in some way but rest one is different. Choose the one which is different from the other.

Options

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

Answer

To solve the problem of identifying the number that is different from the others among the four given numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: Let's denote the four numbers as A, B, C, and D. For this example, we will use the numbers 8, 15, 31, and 57.

2. **Check the Pattern**: We need to check if there is a common pattern among three of the numbers. The pattern we will look for is whether the numbers can be expressed in the form \(2^n - 1\), where \(n\) is a positive integer.

3. **Evaluate Each Number**:
- **For 8**:
- \(2^3 = 8\)
- Therefore, \(8 = 2^3\) and \(8 - 1 = 7\). This fits the pattern.
- **For 15**:
- \(2^4 = 16\)
- Therefore, \(15 = 2^4 - 1\). This fits the pattern.
- **For 31**:
- \(2^5 = 32\)
- Therefore, \(31 = 2^5 - 1\). This fits the pattern.
- **For 57**:
- We check if 57 can be expressed as \(2^n - 1\):
- There is no integer \(n\) such that \(2^n - 1 = 57\). Thus, 57 does not fit the pattern.

4. **Conclusion**: Since 8, 15, and 31 can all be expressed in the form \(2^n - 1\) while 57 cannot, we conclude that 57 is the odd one out.

### Final Answer:
The number that is different from the others is **57**.

---