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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

Add 9.

Subtract 3.

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

Multiply by 2, then subtract 5.

1 answer

To determine which rule makes all of the given input-output pairs true, we can evaluate each potential rule against the input-output pairs provided:

  1. Add 9.

    • 14 + 9 = 23 (True)
    • 7 + 9 = 16 (False)
    • 2 + 9 = 11 (False)
    • 100 + 9 = 109 (False)

    Does not work.

  2. Subtract 3.

    • 14 - 3 = 11 (False)
    • 7 - 3 = 4 (False)
    • 2 - 3 = -1 (True)
    • 100 - 3 = 97 (False)

    Does not work.

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

    • 14 < 50: 14 + 9 = 23 (True)
    • 7 < 50: 7 + 9 = 16 (False)
    • 2 < 50: 2 + 9 = 11 (False)
    • 100 > 50: 100 + 95 = 195 (True)

    Does not work.

  4. Multiply by 2, then subtract 5.

    • 14: (14 * 2) - 5 = 28 - 5 = 23 (True)
    • 7: (7 * 2) - 5 = 14 - 5 = 9 (True)
    • 2: (2 * 2) - 5 = 4 - 5 = -1 (True)
    • 100: (100 * 2) - 5 = 200 - 5 = 195 (True)

    Works for all pairs.

Therefore, the rule that makes all of the input-output pairs true is:

Multiply by 2, then subtract 5.