Zarrolou I think the answer should be C.
Statement 1 can be made false as well. Consider this example:
Largest number is 21. Second largest 13. Their sum will be 34. Other numbers can be 10,12,12,12. As the average of 5 numbers is 16 then their sum will be 80. These numbers satisfy all constraints as 10+12+12+12+13+21 = 80 averaging to 16. And nowhere does the question mention that numbers should be distinct.
Hence the answer is NO.
Similarly we can get a Yes answer. let largest number be 21 and second largest 14 to sum to 35. rest of numbers can be 10,11,12,12.
Statement 2 you showed already to be insufficient.
C) Middle number 16 then Second largest lets say is smallest (16) and largest is greater than 20 hence (21). then smallest sum will be 37.
So we will have a definite Yes answer
Bunuel correct me if I am wrong