Question

Which rules would make this input-output pair true?
input
6
rule
Input Output Arrow
?
Input Output Arrow
output
12
Could be a rule for this input-output pair Could not be a rule for this input-output pair
Multiply by 2, then add 3.
Multiply by 2.
If even, write 19. If odd, subtract 3.
Write 12.
Add 11.
Subtract 3, then multiply by 4.

Answer 1

To determine which rules would make the input-output pair of 6 producing an output of 12 true, we can evaluate each of the proposed rules:

1. **Multiply by 2, then add 3.**
- Calculation: \(6 \times 2 + 3 = 12 + 3 = 15\)
- **Output: 15 (Not equal to 12)**
- **Could not be a rule for this input-output pair.**

2. **Multiply by 2.**
- Calculation: \(6 \times 2 = 12\)
- **Output: 12 (Equal to 12)**
- **Could be a rule for this input-output pair.**

3. **If even, write 19. If odd, subtract 3.**
- Since 6 is even, according to the rule, the output would be 19.
- **Output: 19 (Not equal to 12)**
- **Could not be a rule for this input-output pair.**

4. **Write 12.**
- This rule directly specifies the output as 12 regardless of the input.
- **Output: 12 (Equal to 12)**
- **Could be a rule for this input-output pair.**

5. **Add 11.**
- Calculation: \(6 + 11 = 17\)
- **Output: 17 (Not equal to 12)**
- **Could not be a rule for this input-output pair.**

6. **Subtract 3, then multiply by 4.**
- Calculation: \((6 - 3) \times 4 = 3 \times 4 = 12\)
- **Output: 12 (Equal to 12)**
- **Could be a rule for this input-output pair.**

**Summary:**

- Could be a rule for this input-output pair:
- Multiply by 2.
- Write 12.
- Subtract 3, then multiply by 4.

- Could not be a rule for this input-output pair:
- Multiply by 2, then add 3.
- If even, write 19. If odd, subtract 3.
- Add 11.