2022 AMC 8 Problems/Problem 12
Contents
Problem
The arrows on the two spinners shown below are spun. Let the number equal times the number on Spinner , added to the number on Spinner . What is the probability that is a perfect square number?
Solution 1
First, we calculate that there are a total of possibilities. Now, we list all of two-digit perfect squares. and 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.
~MathFun1000
Solution 2
There are total possibilities of . We know , which is a number from spinner , and is a number from spinner . Also, notice that there are no perfect squares in the s or s, so only values of N work, namely and . Hence, .
~MrThinker
Solution 3
Just try them!
- If we spin a 5 on the first spinner, there are no solutions.
- If we spin a 6 on the first spinner, there is one solution (64).
- If we spin a 7 on the first spinner, there are no solutions.
- If we spin an 8 on the first spinner, there is one solution (81).
Therefore, there are 2 solutions and total possibilities, so
~ligonmathkid2
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
https://youtu.be/Ij9pAy6tQSg?t=1008
~Interstigation
Video Solution
https://youtu.be/p29Fe2dLGs8?t=58
~STEMbreezy
Video Solution
~savannahsolver
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.