Answer :
The true statements are: 1, 4, and 6.
Let's break down the statements and check their validity:
1. In January of 2005, Leonardo was 3.
- This statement doesn't contradict any given information, as it's consistent with the age of Leonardo in 2005 stated in the problem.
- True.
2. In January of 2005, Donatello was 23.
- If Donatello was one more than eleven times as old as Leonardo in January 2005, and Leonardo was 3, then Donatello's age should indeed be \(11 \times 3 + 1 = 34\), not 23.
- Not true.
3. In January of 2014, Leonardo was 15.
- We can't directly confirm or deny this statement based on the information provided. However, if Donatello was seven more than three times as old as Leonardo in 2014, and Donatello was 43, then Leonardo's age should be \(\frac{(43 - 7)}{3} = 12\), not 15.
- Not true.
4. In January of 2014, Donatello was 43.
- If Donatello was seven more than three times as old as Leonardo in January 2014, and Leonardo was 12 (as derived above), then Donatello's age should be \(3 \times 12 + 7 = 43\).
- True.
5. Leonardo is older than Donatello.
- Based on the information provided, in January 2014, Donatello was 43, while Leonardo was 12. Hence, Leonardo is not older than Donatello.
- Not true.
6. Donatello is older than Leonardo.
- Donatello being 43 in January 2014 and Leonardo being 12 in January 2014 confirms that Donatello is indeed older than Leonardo.
- True.
So, the true statements are: 1, 4, and 6.
