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

Add 9.

Subtract 3.

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

Multiply by 2, then subtract 5.

Answer 1

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.**