Question: Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90?
We want to find out if total people registered > (90 * 6) = 540
Statement 1: For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.
The least number of people registered in a day is at least 80.
But out of 6 days, 4 days with the greatest number of registration had a record of 100 per day on the average.
Assuming that the remaining 2 days had a registration of at least 80 per day;
Total people registered = (100 * 4) + (80 * 2) = 400 + 160 = 560
Therefore, the total people registered is greater than 540, statement 1 is SUFFICIENT.

Statement 2: For the 3 days the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.
This statement implies that at least, 85 people will be registered for the 6-day.
So minimum registered people = 85*6 = 510
$$Hence,\ total\ people\ registered\ge510$$
If the total people registered = 510, then it is < 540
But if the total people registered 610, then it is > 540.
Therefore, the information provided is not enough to arrive at a definite answer. Hence, statement 2 is NOT SUFFICIENT.

Since statement 1 alone is SUFFICIENT. Answer = option A