Problems(2)
Jerry and Aaron both pick two integers from 1 to 6, inclusive, and independently and secretly tell their numbers to Dennis. Dennis then announces, "Aaron's number is at least three times Jerry's number." Aaron says, "I still don't know Jerry's number." Jerry then replies, "Oh, now I know Aaron's number." What is the sum of their numbers?<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>7<spanclass=′latex−bold′>(E)</span>8 2022 A Individual
How many ways are there to color each of the 8 cells below red or blue such that no two blue cells are adjacent?
[asy]
size(3cm);
draw((0,0)--(4,0)--(4,1)--(0,1)--(0,0));
draw((1,-1)--(1,2)--(3,2)--(3,-1)--(1,-1));
draw((2,-1)--(2,2));
[/asy]<spanclass=′latex−bold′>(A)</span>48<spanclass=′latex−bold′>(B)</span>50<spanclass=′latex−bold′>(C)</span>52<spanclass=′latex−bold′>(D)</span>54<spanclass=′latex−bold′>(E)</span>56 2022 B Individual