Each correctional facility in a certain state has the same

1 is sufficient, let's denote x - total number of female interns in the state, y - total number of male interns in the state, d - percent of the male interns in the considered facility. We know d is between 18% and 22%.

Total number of facilities is (x+y)/(22%*x+d*y) = n, it's easy to show that 4 < n < 6

(x+y)/(22%*x+d*y) <= (x+y)/(22%*x + 18%*d) < (x+y)/(18%*x+18%*y) = 1/18% < 6
(x+y)/(22%*x + d*y) >= (x+y)/(22%*x + 22%*y) = 1/22% > 4

Therefore, n = 5, then d < 20%


2 is sufficient -> there are at least 4 other facilities or 5 total (22%*4 = 88% < 100%), in each facility there are more male interns than in the considered facility. Therefore percentage of male interns in the considered facility is below 20% of the male interns in the state