21 : 462 :: ?

Options

A. 30: 931
B. `23: 552`
C. `17 : 296`
D. `13 : 142`

Explanation

To solve the analogy problem 21 : 462 :: ? : ?, we need to identify the relationship between the numbers 21 and 462, and then apply the same relationship to find the missing pair.

### Step-by-Step Solution:

1. **Identify the Relationship**:
We start with the pair 21 and 462. We need to find out how 21 relates to 462.

2. **Check Multiplication**:
Let's see if 462 can be obtained by multiplying 21 by a certain number:
\[ 21 \times 22 = 462 \]
So, we can say that 462 is obtained by multiplying 21 by 22.

3. **Apply the Same Logic**:
Now, we need to find a number (let's call it \( x \)) such that when we multiply it by 22, we can find the second number in the pair. We can represent this as:
\[ x \times 22 \]

4. **Choose a Value for \( x \)**:
Let's choose a number for \( x \). For example, if we take \( x = 30 \):
\[ 30 \times 22 = 660 \]
So, the pair would be 30 : 660.

5. **Verify the Relationship**:
We need to ensure that the relationship holds true. If we take \( x = 30 \) and apply the same multiplication:
\[ 30 \times 22 = 660 \]
This confirms that the relationship holds.

6. **Final Answer**:
Therefore, the complete analogy is:
\[ 21 : 462 :: 30 : 660 \]