Select the related number from the given alternatives
2:10: : 26 : ?`

Options

A. 50
B. 36
C. 42
D. 20

Explanation

To solve the problem, we need to identify the relationship between the numbers given in the pairs. The first pair is 2 and 10, and the second number is 26. We need to find the number that corresponds to 26 in the same way that 10 corresponds to 2.

### Step-by-Step Solution:

1. **Identify the first pair**: The first pair is (2, 10).
- Here, we notice that 10 can be derived from 2 by using the formula:
\[ n^2 + 1 \]
- Where \( n \) is an odd number starting from 1. For the first pair:
\[ 1^2 + 1 = 1 + 1 = 2 \]

2. **Identify the second pair**: The second number is 26.
- We need to find the odd number that, when squared and added to 1, gives us 26.
- Let's check the next odd number after 1, which is 3:
\[ 3^2 + 1 = 9 + 1 = 10 \]
- The next odd number is 5:
\[ 5^2 + 1 = 25 + 1 = 26 \]

3. **Find the next odd number**: The next odd number after 5 is 7.
- Now we apply the same formula to 7:
\[ 7^2 + 1 = 49 + 1 = 50 \]

4. **Conclusion**: Therefore, the number that corresponds to 26 using the same pattern is 50.

### Final Answer:
The related number is **50**.