MathDB

12

Part of 2022 AMC 8 -

Problems(1)

Two Spinners (2022 AMC 8 P12)

Source:

1/25/2022
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]
AMC 82022 AMC 8