Which rules would make this input-output pair true?

Question

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.