Complete the analogy `3 : 11 : : 7 :` ____

Options

A. 29
B. 18
C. 24
D. 51

Answer

To solve the analogy `3 : 11 :: 7 : ?`, we need to find the relationship between the numbers in the first pair (3 and 11) and then apply that same relationship to the second pair (7 and the unknown).

### Step-by-Step Solution:

1. **Identify the relationship in the first pair (3 and 11)**:
- We can express 11 in terms of 3. One way to do this is to use the formula:
\[ n^2 + 2 \]
- For 3:
\[ 3^2 + 2 = 9 + 2 = 11 \]

2. **Apply the same relationship to the second number (7)**:
- Now, we will use the same formula for 7:
\[ 7^2 + 2 \]

3. **Calculate \(7^2 + 2\)**:
- First, calculate \(7^2\):
\[ 7^2 = 49 \]
- Then add 2:
\[ 49 + 2 = 51 \]

4. **Conclusion**:
- Therefore, the missing number in the analogy is 51.

So, the complete analogy is:
\[ 3 : 11 :: 7 : 51 \]

### Final Answer:
The answer is **51**.