AMC12 2004 B

AMC12 2004 B · Q1

AMC12 2004 B · Q1. It mainly tests Arithmetic sequences basics.

At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice?

上周每次篮球练习，Jenny 投中的罚球数是前一次练习的两倍。第五次练习她投中了 48 个罚球。她第一次练习投中了多少个罚球？

(A) 3 3

(B) 6 6

(D) 12 12

(E) 15 15

Answer

Correct choice: (A)

正确答案：（A）

Solution

Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made $\frac{1}{2} \cdot 48 = 24$ free throws, on the third $12$, on the second $6$, and on the first $3 \Rightarrow \mathrm{(A)}$. Because there are five days, or four transformations between days (day 1 $\rightarrow$ day 2 $\rightarrow$ day 3 $\rightarrow$ day 4 $\rightarrow$ day 5), she makes $48 \cdot \frac{1}{2^4} = \boxed{\mathrm{(A)}\ 3}$

每次练习 Jenny 投中的罚球数都是下一次练习的一半。因此第四次练习她投中了 $\frac{1}{2} \cdot 48 = 24$ 个罚球，第三次是 $12$ 个，第二次是 $6$ 个，第一次是 $3 \Rightarrow \mathrm{(A)}$。因为共有五次练习，也就是有四次从一次到下一次的倍增（第 1 次 $\rightarrow$ 第 2 次 $\rightarrow$ 第 3 次 $\rightarrow$ 第 4 次 $\rightarrow$ 第 5 次），所以第一次为 $48 \cdot \frac{1}{2^4} = \boxed{\mathrm{(A)}\ 3}$

Topics

AR.012 Arithmetic sequences basics