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Which rules would make this input-output pair true?

input
11
rule
Input Output Arrow
?
Input Output Arrow
output
23
Could be a rule for this input-output pair Could not be a rule for this
input-output pair
Write 11.
Add 12.
Multiply by 2, then add 1.
If even, add 12. If odd, add 10.
Multiply by 3, then subtract 10.

1 answer

To determine which rules could make the input-output pair of 11 leading to 23 true, we can evaluate each rule based on the operations it describes.

  1. Write 11: This rule does nothing to the input. The output remains 11, so this cannot be true.

  2. Add 12:

    • Input: 11
    • Output: 11 + 12 = 23
    • This rule is valid.

  3. Multiply by 2, then add 1:

    • Input: 11
    • Output: (11 * 2) + 1 = 22 + 1 = 23
    • This rule is valid.

  4. If even, add 12. If odd, add 10:

    • Since 11 is odd, we add 10.
    • Input: 11
    • Output: 11 + 10 = 21, not 23.
    • This rule is not valid.

  5. Multiply by 3, then subtract 10:

    • Input: 11
    • Output: (11 * 3) - 10 = 33 - 10 = 23
    • This rule is valid.

Based on these evaluations, the rules that could make the input-output pair true are:

  • Add 12
  • Multiply by 2, then add 1
  • Multiply by 3, then subtract 10

So, summarizing:

  • Could be a rule for this input-output pair:

    • Add 12
    • Multiply by 2, then add 1
    • Multiply by 3, then subtract 10

  • Could not be a rule for this input-output pair:

    • Write 11
    • If even, add 12. If odd, add 10.