If $(n - 1)$ is an odd number, what are the two other odd numbers nearest to it?

### Concept & Logic Consecutive odd numbers are always separated by a constant difference of exactly 2. To find the nearest odd numbers to any given odd expression, you simply subtract 2 for the preceding odd number and add 2 for the succeeding odd number. ### Step-by-Step Solution **Given:** * The core expression is $(n - 1)$. * $(n - 1)$ is an odd number. **Calculation / Deduction:** To find the immediately preceding odd number, subtract $2$ from the given odd number: $$\text{Previous Odd} = (n - 1) - 2$$ $$\text{Previous Odd} = n - 3$$ To find the immediately succeeding odd number, add $2$ to the given odd number: $$\text{Next Odd} = (n - 1) + 2$$ $$\text{Next Odd} = n + 1$$ Therefore, the two nearest odd numbers are $n - 3$ and $n + 1$. ### Exam Strategy & Shortcut Use real numbers to bypass the algebra. Let $(n - 1) = 5$, which means $n = 6$. The nearest odd numbers to $5$ are $3$ and $7$. Now substitute $n = 6$ into the options. Option (c) gives $6 - 3 = 3$ and $6 + 1 = 7$. This matches our numerical logic perfectly and guarantees accuracy. ### Common Pitfall Students often misread the question and add or subtract 1 instead of 2. Doing so yields $(n - 2)$ and $n$, which represent consecutive integers (an even/odd mix), rather than consecutive *odd* numbers. ### Final Answer Therefore, the correct answer is **$n - 3, n + 1$**.