AMC 8 2022 Problem 12
AMC8 2022 年第 12 题
概率★★★☆☆
The arrows on the two spinners shown below are spun. Let the number N equal 10 times the number on Spinner , added to the number on Spinner . What is the probability that N is a perfect square number?
下图所示的两个转盘上的箭头可自由旋转。数 N 等于 10 乘以转盘 A 上箭头所指的数，再加上转盘 B 上箭头所指的数。问 N 是完全平方数的概率是多少？
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- B.
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正确答案 · Correct Answer
B
解析 · Solution
Solution 1
First, we calculate that there are a total of 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 probability that the number formed by the two spinners is a perfect square.
There are total possibilities of . We know N=10A+B, which is a number from spinner , and is a number from spinner . Also, notice that there are no perfect squares in the 50 s or 70 s, so only 4-2=2 values of N work, namely 64 and 81. Hence, .
We can see that the smallest number on the spinner 1 is 5. Possibilities for 5 are 51,52,53, and 54 Second one is 6 in which we get 61,62,63,64. We see that 64 is a square number. The next number is 7. Possibilities are 71,72,73, and 74. None of them are squares. Finally, we have 8. 81,82,83, and 84 are the numbers possible. 81 is a perfect square. As our trusty probability formula tells us, probability is the number of desired outcomes over possible outcomes. The possible outcomes are 16 and the desired outcomes are 2. The fraction is . In simplest terms, it is . Bringing to answer choice (B)
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