In the questions, select the pair in which the numbers are similarly related as in the given pair.
9: 512 :: ?:?

Options

A. `7:206`
B. `6: 126`
C. ` 5: 65`
D. `10: 729 `

Explanation

To solve the analogy problem, we need to identify the relationship between the numbers in the given pair (9: 512) and apply the same relationship to find the correct pair from the options provided.

### Step-by-Step Solution:

1. **Identify the relationship in the given pair (9: 512)**:
- We start with the first number, which is 9.
- We subtract 1 from 9:
\[ 9 - 1 = 8 \]
- Next, we cube the result:
\[ 8^3 = 512 \]
- Therefore, the relationship is:
\[ \text{If } x = 9, \text{ then } (x - 1)^3 = 512 \]

2. **Apply the same relationship to the options**:
- We will check each option to see if it follows the same pattern.

**Option 1: 7: 206**
- Calculate:
\[ 7 - 1 = 6 \]
\[ 6^3 = 216 \quad (\text{not } 206) \]
- This option is eliminated.

**Option 2: 6: 126**
- Calculate:
\[ 6 - 1 = 5 \]
\[ 5^3 = 125 \quad (\text{not } 126) \]
- This option is eliminated.

**Option 3: 5: 65**
- Calculate:
\[ 5 - 1 = 4 \]
\[ 4^3 = 64 \quad (\text{not } 65) \]
- This option is eliminated.

**Option 4: 10: 729**
- Calculate:
\[ 10 - 1 = 9 \]
\[ 9^3 = 729 \]
- This option follows the same pattern as the original pair.

3. **Conclusion**:
- The correct answer is option 4: 10: 729.