Which of the following numbers is not divisible by 18?

### Concept & Strategy For a number to be divisible by a composite number like $18$, it must be divisible by its co-prime factors, which are $2$ and $9$. $$18 = 2 \times 9$$ Therefore, the number must be even (divisible by $2$) and the sum of its digits must be a multiple of $9$. ### Step-by-Step Solution We are looking for the number that is **not** divisible by $18$. The easiest way to break this is to find a number that fails the simplest divisibility rule first. * **Test for divisibility by 2:** A number is divisible by $2$ if its unit digit is $0, 2, 4, 6, \text{or} 8$. * **Examine the options:** (a) $34056$ ends in $6$ (Even - Divisible by $2$) (b) $50436$ ends in $6$ (Even - Divisible by $2$) (c) $54036$ ends in $6$ (Even - Divisible by $2$) (d) $65043$ ends in $3$ (Odd - **Not divisible by 2**) Since $65043$ is an odd number, it cannot possibly be a multiple of an even number like $18$. We do not even need to check the rule for $9$. ### Exam Strategy & Shortcut Always check divisibility by $2$ or $5$ first before checking sums ($3$ or $9$) because they only require looking at the final digit. This visual scan takes less than two seconds, allowing you to bypass tedious addition. ### Common Pitfall The most common trap is ignoring the unit digit and immediately adding up the sum of the digits for all four options. While $65043$ ($6+5+0+4+3=18$) is technically divisible by $9$, doing this calculation wastes precious exam time. ### Final Answer Therefore, the correct answer is **65043**.