BTGmoderatorLU wrote:Source: Manhattan Prep
During a week-long sale at a car dealership, the most number of cars sold on any one day was 12. If at least 2 cars were sold each day, was the average daily number of cars sold during that week more than 6?
1. During that week, the second smallest number of cars sold on any one day was 4.
2. During that week, the median number of cars sold was 10.
The OA is B.
Given: Out of 7 days in the week, at least 2 cars sold per day and at the most 12 cars sold per day.
Question: Was the average daily number of cars sold during that week more than 6?
Let's take each statement one by one.
1. During that week, the second smallest number of cars sold on any one day was 4.
Since 4 is the second smallest, smallest can be 2 or 3.
Case 1: Say the set of the number of cars sold is: {2, 4, 4, 4, 4, 4, 12}. Average = 34/7 < 6. The answer is No.
Case 2: Say the set of the number of cars sold is: {2, 4, 12, 12, 12, 12, 12}. Average = 66/7 > 6. The answer is Yes.
No unique answer. Insufficient.
2. During that week, the median number of cars sold was 10.
Since the week is of 7 days, the middle-most term would be the 3rd term. Thus, the value of the 3rd term = 10.
Let's assume the minimum possible sale scenario.
The set arranged in the ascending order would be: {2, 2, 2,
10, 10, 10, 12}. Average = 48/7 > 6. The answer is Yes.
Since above is the minimum possible sale scenario, other scenarios would definitely render higher sale than 48 cars in the week. Thus, we can conclude that the average daily number of cars sold during that week was more than 6. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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