Explanation:

To determine if the number 143b203a is divisible by 15, it must be divisible by both 3 and 5. Let's break down the criteria:

- Divisibility by 5: The last digit, 'a', must be 0 or 5.

- Divisibility by 3: The sum of all digits, \(1 + 4 + 3 + b + 2 + 0 + 3 + a\) should be divisible by 3.

Consider values for 'a' and 'b':

- If \(a = 0\):

- Sum: \(13 + b\).

- If divisibly by 3: \(b = 2\) (15), \(b = 5\) (18), \(b = 8\) (21).

- Max \(a + b = 0 + 8 = 8\).

- If \(a = 5\):

- Sum: \(18 + b\).

- If divisible by 3: \(b = 0\) (18), \(b = 3\) (21), \(b = 6\) (24), \(b = 9\) (27).

- Max \(a + b = 5 + 9 = 14\).

Based on these calculations:

- Option 1 (15): No such combination for 15.

- Option 2 (17): No such combination for 17.

- Option 3 (16): No such combination for 16.

- Option 4 (14): Yes, when a = 5 and b = 9.