Difference between revisions of "2022 AMC 8 Problems/Problem 20"

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-==Solution 5 (Super fast! No algebra and no testing any of the answer choices!)==
-The sum of the numbers in each column and row should be <math>5+(-1)+8=12</math>. If we look at the <math>1^{\text{st}}</math> column, the gray squares (shown below) sum to <math>12-(-2)=14</math>.
-<asy>
-draw((3,3)--(-3,3));
-draw((3,1)--(-3,1));
-draw((3,-3)--(-3,-3));
-draw((3,-1)--(-3,-1));
-draw((3,3)--(3,-3));
-draw((1,3)--(1,-3));
-draw((-3,3)--(-3,-3));
-draw((-1,3)--(-1,-3));
-label((-2,2),"$-2$");
-label((0,2),"$9$");
-label((2,2),"$5$");
-label((2,0),"$-1$");
-label((2,-2),"$8$");
-label((-2,-2),"$x$");
-filldraw((-3,-3)--(-1,-3)--(-1,-1)--(-3,-1)--cycle, lightgray, black+linewidth(1));
-filldraw((-1,-1)--(-3,-1)--(-3,1)--(-1,1)--cycle, lightgray, black+linewidth(1));
-label(scale(1)*"All credits for original unedited asymptote for the problem go to whoever made the asymptote in the 'Problem' section.", (-0,-5), S);
-</asy>
-'''If''' square <math>x</math> has to be '''greater than or equal to''' the three blank squares, then the least <math>x</math> can be is half the sum of the value of the gray squares, which is <math>14\div2=7</math>. But square <math>x</math> has to be '''greater than''' and '''''not''''' '''greater than or equal to''' the three blank squares, so the least <math>x</math> can be is <math>7+1=8</math>. Testing for the other rows and columns (it might be smaller than the other two squares!), we find that the smallest <math>x</math> can be is indeed <math>8</math>; the other two squares are less than <math>8</math>. Therefore, the answer is <math>\boxed{\text{(D) }8}</math>.
-~ JoyfulSapling
 ==Video Solution by Math-X (First understand the problem!!!)==
 https://youtu.be/oUEa7AjMF2A?si=Bbea8RWE2sMWN6xl&t=3643

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Difference between revisions of "2022 AMC 8 Problems/Problem 20"

Revision as of 20:35, 7 September 2025

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Video Solution by Math-X (First understand the problem!!!)

Video Solution (🚀Super Fast. Just 1 min!🚀)

Video Solution

Video Solution

Video Solution

Video Solution

Video Solution