AMC8 2022

AMC8 2022 · Q12

AMC8 2022 · Q12. It mainly tests Probability (basic), Perfect squares & cubes.

The arrows on the two spinners shown below are spun. Let the number $N$ equal $10$ times the number on Spinner $\text{A}$, added to the number on Spinner $\text{B}$. What is the probability that $N$ is a perfect square number?

下面两个转盘上的箭头转动。让数字$N$等于转盘A上的数字乘以10，加上转盘B上的数字。$N$是完全平方数的概率是多少？

(A) ~\dfrac{1}{16} ~\dfrac{1}{16}

(B) ~\dfrac{1}{8} ~\dfrac{1}{8}

(D) ~\dfrac{3}{8} ~\dfrac{3}{8}

(E) ~\dfrac{1}{2} ~\dfrac{1}{2}

Answer

Correct choice: (B)

正确答案：（B）

Solution

First, we calculate that there are a total of $4\cdot4=16$ possibilities. Now, we list all of two-digit perfect squares. $64$ and $81$ are the only ones that can be made using the spinner. Consequently, there is a $\frac{2}{16}=\boxed{\textbf{(B) }\dfrac{1}{8}}$ probability that the number formed by the two spinners is a perfect square.

总共有$4\times4=16$种可能。现在，列出所有两位数的完全平方数。只有$64$和$81$可以用转盘组成。因此，有$\frac{2}{16}=\boxed{\textbf{(B) }\dfrac{1}{8}}$的概率。

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