## During a 6-day local trade show…

## Solution:

We are given that during a 6-day trade show, the least number of people registered in a single day was 80. We need to determine whether the average number of people registered per day was greater than 90. We use the formula for the average, as follows:

average = sum/quantity

90 = sum/6

540 = sum

A sum of 540 would yield an average of 90. Thus, we need to determine whether the sum of the number of people registered for the 6 days was greater than 540.

**Statement One Alone: **

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

It follows that the sum for the 4 days with the greatest number of people is 4 x 100 = 400. We also were originally given that the least number of people registered in a single day was 80. Thus, at the very least, the sum for the number of people registered for the 6 days is 400 + 80 + 80 = 560 people. We can now answer yes, the average was greater than 90 for the 6 days; statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

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

It follows that the sum for the 3 days with the smallest number of people is 3 x 85 = 255. However, the average number of people registered per day for the 6-day period may or may not be more than 90 (i.e., the total number of people registered may or may not be more than 540). For example, if the remaining three days have an average of 90 people, then the total number of people registered is (3 x 85) + (3 x 90) = 255 + 270 = 525, which is less than 540. On the other hand, if the remaining three days have an average of 100 people, then the total number of people registered is (3 x 85) + (3 x 100) = 255 + 300 = 555, which is more than 540. Thus, statement two alone is not sufficient to answer the question.

**Answer: A **