MathDB
Two Spinners (2022 AMC 8 P12)

Source:

January 25, 2022
AMC 82022 AMC 8

Problem Statement

The arrows on the two spinners shown below are spun. Let the number NN equal 10 times the number on Spinner AA, added to the number on Spinner BB. What is the probability that NN is a perfect square number?
<spanclass=′latex−bold′>(A)</span> 116<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 38<spanclass=′latex−bold′>(E)</span> 12<span class='latex-bold'>(A)</span> ~\dfrac{1}{16}\qquad<span class='latex-bold'>(B)</span> ~\dfrac{1}{8}\qquad<span class='latex-bold'>(C)</span> ~\dfrac{1}{4}\qquad<span class='latex-bold'>(D)</span> ~\dfrac{3}{8}\qquad<span class='latex-bold'>(E)</span> ~\dfrac{1}{2}\qquad
[asy] //diagram by pog give me 1 billion dollars for this size(6cm); usepackage("mathptmx"); filldraw(arc((0,0), r=4, angle1=0, angle2=90)--(0,0)--cycle,mediumgray*0.5+gray*0.5); filldraw(arc((0,0), r=4, angle1=90, angle2=180)--(0,0)--cycle,lightgray); filldraw(arc((0,0), r=4, angle1=180, angle2=270)--(0,0)--cycle,mediumgray); filldraw(arc((0,0), r=4, angle1=270, angle2=360)--(0,0)--cycle,lightgray*0.5+mediumgray*0.5); label("55", (-1.5,1.7)); label("66", (1.5,1.7)); label("77", (1.5,-1.7)); label("88", (-1.5,-1.7)); label("Spinner A", (0, -5.5)); filldraw(arc((12,0), r=4, angle1=0, angle2=90)--(12,0)--cycle,mediumgray*0.5+gray*0.5); filldraw(arc((12,0), r=4, angle1=90, angle2=180)--(12,0)--cycle,lightgray); filldraw(arc((12,0), r=4, angle1=180, angle2=270)--(12,0)--cycle,mediumgray); filldraw(arc((12,0), r=4, angle1=270, angle2=360)--(12,0)--cycle,lightgray*0.5+mediumgray*0.5); label("11", (10.5,1.7)); label("22", (13.5,1.7)); label("33", (13.5,-1.7)); label("44", (10.5,-1.7)); label("Spinner B", (12, -5.5)); [/asy]
Back to ProblemsView on AoPS