Problems(1)
The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number x in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of x?
[asy]
unitsize(0.5cm);
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");
[/asy]
<spanclass=′latex−bold′>(A)</span>−1<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>9 2022 AMC 8