Which one of the following numbers is divisible by 3?

### Concept & Strategy The fundamental rule for divisibility by $3$ states that a number is divisible by $3$ if the sum of its individual digits is a multiple of $3$. ### Step-by-Step Solution Let us test the sum of the digits for each provided option to find the valid multiple of $3$: * **Option (a) 4006020:** Sum: $4 + 0 + 0 + 6 + 0 + 2 + 0 = 12$ Since $12$ is perfectly divisible by $3$ ($12 / 3 = 4$), this entire number is divisible by $3$. * **Option (b) 2345678:** Sum: $2 + 3 + 4 + 5 + 6 + 7 + 8 = 35$ $35$ is not a multiple of $3$. * **Option (c) 2876423:** Sum: $2 + 8 + 7 + 6 + 4 + 2 + 3 = 32$ $32$ is not a multiple of $3$. * **Option (d) 9566003:** Sum: $9 + 5 + 6 + 6 + 0 + 0 + 3 = 29$ $29$ is not a multiple of $3$. ### Exam Strategy & Shortcut Use the "digit cancellation" or "casting out 3s" method to calculate faster. Instead of adding all digits, cross out any $3, 6, 9$, or combinations of digits that add to a multiple of $3$. For option (a): $4006020$. Cross out $6$. You are left with $4$ and $2$. $4 + 2 = 6$, which is a multiple of $3$. This guarantees the number is divisible without performing long addition. ### Common Pitfall The main risk here is simple arithmetic errors when adding up long strings of digits (like in option b or c). Using the cancellation shortcut prevents these basic addition mistakes. ### Final Answer Therefore, the correct answer is **4006020**.