BlueDragon2010 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 number registered per day was 100.
2) For the 3 days with the smallest number of people registered, the average number registered per day was 85.
This is a weighted average problem.
If we understand how weighted averages work, almost no math is required.
Statement 1: For the 4 days with the greatest number of people registered, the average number registered per day was 100.
Since the average for more than 1/2 of the 6 days is 100, and the LEAST possible average for the remaining days is 80, the average for all 6 days must be weighted CLOSER TO 100 THAN TO 80.
Thus, the average for all 6 days must be greater than 90 (the halfway point between 80 and 100).
SUFFICIENT.
Statement 2: For the 3 days with the smallest number of people registered, the average number registered per day was 85.
If the average for the other 3 days is 86, then the average for all 6 days will be less than 90.
If the average for the other 3 days is 1000, then the average for all 6 days will be greater than 90.
INSUFFICIENT.
The correct answer is
A.
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