If the numbers from $1$ to $24$, which are divisible by $2$ are arranged in descending order, which number will be at the 8th place from the bottom?

### Concept & Logic When an arithmetic progression is arranged in descending order, counting from the bottom is mathematically identical to counting the same sequence in its natural ascending order. ### Step-by-Step Solution **Given:** * The set of numbers is integers from $1$ to $24$ that are divisible by $2$ (even numbers). * The arrangement is in descending order (highest to lowest). * We need to find the 8th number from the bottom. **Calculation / Deduction:** Identify the even numbers between $1$ and $24$: $2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24$ Arranging them in descending order forms this sequence: $24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2$ The "bottom" of a descending list is simply the smallest number, which is $2$. Counting 8 positions up from the bottom (i.e., treating $2$ as the 1st position): 1st: 2 2nd: 4 3rd: 6 ... The $n$-th number from the bottom is simply $2 \times n$. For the 8th place: $2 \times 8 = 16$. ### Exam Strategy & Shortcut Skip generating the descending list altogether. Recognize that "8th from the bottom in a descending list of even numbers" is exactly the same as asking for the "8th even number starting from 2". Thus, simply calculate $8 \times 2 = 16$. ### Common Pitfall The most common mistake is counting from the top instead of the bottom. If a student calculates the 8th place from the top, they would perform $24 - (8-1) \times 2 = 10$, and incorrectly choose option (a). Always double-check the direction of the positional request. ### Final Answer Therefore, the correct answer is **16**.