Question

Which rule would make all of these input-output pairs true?
input
Input Output Arrow
rule
Input Output Arrow
output


Input Output
14 23
7 9
2 -1
100 195

If less than 50, add 9. If greater than 50, add 95.

Add 9.

Subtract 3.

Multiply by 2, then subtract 5.

Answer 1

To determine which rule makes all of the given input-output pairs true, we need to evaluate the rules provided against each input in the pair.

Let's analyze the input-output pairs with each suggested rule:

1. **Input: 14, Output: 23**
2. **Input: 7, Output: 9**
3. **Input: 2, Output: -1**
4. **Input: 100, Output: 195**

### Rule 1: If less than 50, add 9. If greater than 50, add 95.
- For **14**:
\(14 < 50\) → \(14 + 9 = 23\) (Correct)

- For **7**:
\(7 < 50\) → \(7 + 9 = 16\) (Incorrect)

- For **2**:
\(2 < 50\) → \(2 + 9 = 11\) (Incorrect)

- For **100**:
\(100 > 50\) → \(100 + 95 = 195\) (Correct)

This rule is incorrect for inputs 7 and 2.

### Rule 2: Add 9.
- For **14**:
\(14 + 9 = 23\) (Correct)

- For **7**:
\(7 + 9 = 16\) (Incorrect)

- For **2**:
\(2 + 9 = 11\) (Incorrect)

- For **100**:
\(100 + 9 = 109\) (Incorrect)

This rule fails for all inputs except 14.

### Rule 3: Subtract 3.
- For **14**:
\(14 - 3 = 11\) (Incorrect)

- For **7**:
\(7 - 3 = 4\) (Incorrect)

- For **2**:
\(2 - 3 = -1\) (Correct)

- For **100**:
\(100 - 3 = 97\) (Incorrect)

This rule fails for 14, 7, and 100.

### Rule 4: Multiply by 2, then subtract 5.
- For **14**:
\(14 \times 2 - 5 = 28 - 5 = 23\) (Correct)

- For **7**:
\(7 \times 2 - 5 = 14 - 5 = 9\) (Correct)

- For **2**:
\(2 \times 2 - 5 = 4 - 5 = -1\) (Correct)

- For **100**:
\(100 \times 2 - 5 = 200 - 5 = 195\) (Correct)

### Conclusion
The **fourth rule** ("Multiply by 2, then subtract 5") makes all input-output pairs true:

- **Input: 14 → Output: 23**
- **Input: 7 → Output: 9**
- **Input: 2 → Output: -1**
- **Input: 100 → Output: 195**

So, the correct rule is: **Multiply by 2, then subtract 5.**