Find the greatest possible value of (a + b) for which the 8-digit number 143b203a is divisible by 15.
Explanation:
143b203a should be divisible by 15.
Hence, it should be divisible by both 5 and 3.
∴ For 143b203a to be divisible by 15, a should be either 0 or 5.
Case 1: a = 0 Now, 143b2030 should be divisible by 3. ∴ Sum of digits = 1 + 4 + 3 + b + 2 + 0 + 3 + 0 = 13 + b should be divisble by 3. Hence, highest value of b can be 8 ∴ Highest value of a + b = 0 + 8 = 8
Case 2: a = 5 Now, 143b2035 should be divisible by 3. ∴ Sum of digits = 1 + 4 + 3 + b + 2 + 0 + 3 + 5 = 18 + b should be divisble by 3. Hence, highest value of b can be 9 ∴ Highest value of a + b = 5 + 9 = 14
Hence, option (d).
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