Question

35.

Read the following conjecture.

Any number that is divisible by 3 is also divisible by 9.

Find a counterexample to show that the conjecture is false.

18

27

48

45

Answer 1

[AI-generated answer — Bot GPT-4o]

To find a counterexample that shows the conjecture "Any number that is divisible by 3 is also divisible by 9" is false, you need to find a number that is divisible by 3 but not divisible by 9.

Let's check each option:

1. **18**:
- 18 ÷ 3 = 6 (18 is divisible by 3)
- 18 ÷ 9 = 2 (18 is divisible by 9)

2. **27**:
- 27 ÷ 3 = 9 (27 is divisible by 3)
- 27 ÷ 9 = 3 (27 is divisible by 9)

3. **48**:
- 48 ÷ 3 = 16 (48 is divisible by 3)
- 48 ÷ 9 ≈ 5.33 (48 is not divisible by 9)

4. **45**:
- 45 ÷ 3 = 15 (45 is divisible by 3)
- 45 ÷ 9 = 5 (45 is divisible by 9)

The number **48** is divisible by 3 but not divisible by 9, making it a counterexample that disproves the conjecture.