9: 80 :: 7 :?

Options

A. 48
B. 50
C. 78
D. 82

Explanation

To solve the analogy problem \(9 : 80 :: 7 : ?\), we need to identify the relationship between the numbers in the first pair and apply the same relationship to the second pair.

### Step-by-Step Solution:

1. **Identify the relationship in the first pair (9 and 80)**:
- Start with the number 9.
- Square it: \(9^2 = 81\).
- Notice that the result is 81, but the second number is 80.
- To find the connection, we subtract 1 from 81:
\[ 81 - 1 = 80 \]
- Therefore, the relationship can be expressed as:
\[ \text{If } x = 9, \text{ then } y = x^2 - 1 \text{ which gives } y = 80. \]

2. **Apply the same relationship to the second pair (7 and ?)**:
- Start with the number 7.
- Square it: \(7^2 = 49\).
- Now, apply the same operation as before by subtracting 1 from 49:
\[ 49 - 1 = 48 \]
- Thus, the value that replaces the question mark is:
\[ ? = 48. \]

3. **Final Answer**:
- Therefore, the complete analogy is:
\[ 9 : 80 :: 7 : 48. \]