Data Sufficiency

During a 6·day local trade show, the least number of people registered in a single day was 80. Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90?

(1) For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.
(2) For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.

The OA is A.

Easy way:

Statement (1):
(80+4*100+x)/6 > 90 ?
480+x > 540
x>60
There would be more than 90 people per day if on the 5th day there were at least 60 people. We know the least number of people registered at any day was 80. Sufficient.

Easy to check:
(80+400+60)/6 = 90 --> 540 = 540
(80+400+70)/6 > 90 --> 550 > 540

Statement (2):
(3*85+x+y)/6 > 90?
255+x+y > 540?
x+y > 285?

Do you know? Me neither. Insufficient.

Has anyone another strategic approach to solving this DS question? Regards!

AAPL wrote:During a 6·day local trade show, the least number of people registered in a single day was 80. Was the average (arithmetic mean) number of people registered per day for the 6 days greater than 90?

(1) For the 4 days with the greatest number of people registered, the average (arithmetic mean) number registered per day was 100.
(2) For the 3 days with the smallest number of people registered, the average (arithmetic mean) number registered per day was 85.

Statement 1:
Average for 4 of the 6 days = 100 per day.
Least possible average for the other 2 days = 80 per day.
Since there are MORE DAYS with an average of 100 per day than with an average of at least 80 per day, the average for all 6 days must be CLOSER TO 100 THAN TO 80.
Thus, the average for all 6 days must be greater than 90.
SUFFICIENT.

Statement 2:
Test EXTREMES.
Case 1: Average for 3 days = 85 per day, average for the other 3 days = 86 per day
In this case, the average for all 6 days is less than 90.
Case 2: Average for 3 days = 85 per day, average for the other 3 days = 10,000 per day
In this case, the average for all 6 days is greater than 90.
Since the answer to the question stem is NO in Case 1 but YES in Case 2, INSUFFICIENT.

The correct answer is A.