Choosing a number related to a given number in the same manner as the two numbers of another given pair are related to each other
8 : 32 :: 10: ?

Options

A. 42
B. 44
C. 45
D. 50

Explanation

To solve the analogy problem \( 8 : 32 :: 10 : ? \), we need to find the relationship between the first pair of numbers (8 and 32) and apply the same relationship to the second pair (10 and the unknown number).

### Step 1: Identify the relationship between 8 and 32
The first step is to analyze how 8 relates to 32.

- We can see that \( 32 \) is derived from \( 8 \) by performing a mathematical operation.
- One way to express this is:
\[ 32 = \frac{8^2}{2} \]
Here, \( 8^2 = 64 \) and when we divide it by \( 2 \), we get \( 32 \).

### Step 2: Apply the same relationship to 10
Now, we will apply the same operation to the number \( 10 \) to find the unknown number.

- We calculate:
\[ ? = \frac{10^2}{2} \]
- First, calculate \( 10^2 \):
\[ 10^2 = 100 \]
- Now divide \( 100 \) by \( 2 \):
\[ ? = \frac{100}{2} = 50 \]

### Conclusion
Thus, the number that corresponds to \( 10 \) in the same relationship as \( 8 \) to \( 32 \) is \( 50 \).

The final answer is:
\[ 10 : 50 \]