Choose the set of numbers from the four alternatives which is similar to the given set.
Given set : (5, 24, 124)

Options

A. (7,50, 343)
B. (5, 14, 124)
C. (3, 8, 26)
D. (4, 16, 63)

Explanation

To solve the problem, we need to identify a pattern in the given set of numbers (5, 24, 124) and then find another set of numbers that follows the same pattern.

### Step-by-Step Solution:

1. **Identify the Pattern in the Given Set:**
- The first number is 5.
- The second number is 24, which can be expressed as \(5^2 - 1\).
- Calculation: \(5^2 = 25\), and \(25 - 1 = 24\).
- The third number is 124, which can be expressed as \(5^3 - 1\).
- Calculation: \(5^3 = 125\), and \(125 - 1 = 124\).

Therefore, the pattern is:
- First number: \(a\)
- Second number: \(a^2 - 1\)
- Third number: \(a^3 - 1\)

2. **Apply the Pattern to the Options:**
- We need to check each option to see if it follows the same pattern.

3. **Check Option 1: (7, 50, 3, 43)**
- First number: 7
- Second number should be \(7^2 - 1 = 49 - 1 = 48\) (not 50)
- Third number should be \(7^3 - 1 = 343 - 1 = 342\) (not 3)
- **Conclusion**: Option 1 does not follow the pattern.

4. **Check Option 2: (5, 14, 124)**
- First number: 5
- Second number should be \(5^2 - 1 = 25 - 1 = 24\) (not 14)
- Third number should be \(5^3 - 1 = 125 - 1 = 124\) (correct)
- **Conclusion**: Option 2 does not follow the pattern.

5. **Check Option 3: (3, 8, 20)**
- First number: 3
- Second number should be \(3^2 - 1 = 9 - 1 = 8\) (correct)
- Third number should be \(3^3 - 1 = 27 - 1 = 26\) (not 20)
- **Conclusion**: Option 3 does not follow the pattern.

6. **Check Option 4: (4, 16, 63)**
- First number: 4
- Second number should be \(4^2 - 1 = 16 - 1 = 15\) (not 16)
- Third number should be \(4^3 - 1 = 64 - 1 = 63\) (correct)
- **Conclusion**: Option 4 does not follow the pattern.

### Final Conclusion:
None of the options provided follow the exact pattern established by the original set (5, 24, 124). Therefore, it appears there might be an error in the options provided or in the interpretation of the question.