Question

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

$\displaystyle \dfrac{1}{16}$

$\displaystyle \dfrac{1}{8}$

$\displaystyle \dfrac{1}{4}$

$\displaystyle \dfrac{3}{8}$

$\displaystyle \dfrac{1}{2}$

Solution:

Spinner A gives the tens digit and Spinner B gives the ones digit. There are $4\cdot4=16$ equally likely two-digit numbers.

The possible perfect squares between $51$ and $84$ are $64$ and $81$ , and both can occur. Thus the probability is $\frac{2}{16}=\frac{1}{8}.$

Thus, the correct answer is B.

2022 AMC 8 Problem 12

Solution:

Problem 12 in Other Years