The total of integers should be 111. Now, 18 the least of all.
Hence, the sum of other two integers must be 93,
In order to maximize the largest number, the middle number and small numbers should be minimized. since smallest number is 18. Therefore, middle number can go as small as 19. Therefore, 93 - 19 = 74 which is the maximum possible value for largest number.
How about minimum possible value for largest number?
Knowing Largest and smallest to be 74 and 18, adding them and dividing by 2 would give 46, which is the largest possible number for the MIDDLE number. Therefore, leading to all values larger than 46 possible values for largest number.

(x+y+18)/3 = 37
x+y = (37)*3-18 = 93
also x>18 and y>18

Assume x = 19, then y = 93-19 = 74 --> greatest possible value of y
Assume x and y are very close together --> x = 46, y=47 --> least possible value of y without y become less than x

So 47 <= y <= 74 --> answer choices C,D,E