Which one of the following numbers is divisible by 15?

### Concept & Strategy For a number to be divisible by a composite number like 15, it must be divisible by its co-prime factors, which are 3 and 5. $$15 = 3 \times 5$$ Therefore, the number must end in 0 or 5 (divisibility by 5), and the sum of its digits must be a multiple of 3 (divisibility by 3). ### Step-by-Step Solution * **Check divisibility by 5:** All four options (17325, 23755, 29515, 30560) end in either 5 or 0. Thus, all are divisible by 5. We must rely on the rule for 3. * **Check divisibility by 3 (Sum of digits):** * Option (a) 17325: $1 + 7 + 3 + 2 + 5 = 18$. (18 is divisible by 3). * Option (b) 23755: $2 + 3 + 7 + 5 + 5 = 22$. (Not divisible by 3). * Option (c) 29515: $2 + 9 + 5 + 1 + 5 = 22$. (Not divisible by 3). * Option (d) 30560: $3 + 0 + 5 + 6 + 0 = 14$. (Not divisible by 3). Only option (a) satisfies both conditions. ### Exam Strategy & Shortcut Use the "digit cancellation" method for the rule of 3 to save time. In option (a) 17325, cancel out the 3 immediately. You are left with 1, 7, 2, and 5. $7 + 2 = 9$ (cancel it). $1 + 5 = 6$ (cancel it). Everything cancels out, meaning it is a perfect multiple of 3 without doing a single large addition. ### Common Pitfall A common mistake is trying to divide large numbers directly by 15. This is highly time-consuming and prone to long-division arithmetic errors. Always break composite numbers down into co-prime rules. ### Final Answer Therefore, the correct answer is **17325**.