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During a week-long sale at a car dealership, the most number

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During a week-long sale at a car dealership, the most number

by BTGmoderatorLU » Thu Oct 25, 2018 2:13 pm

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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.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Oct 25, 2018 11:02 pm

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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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by deloitte247 » Fri Oct 26, 2018 3:38 pm

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Was the average daily number of cars sold during the week more than 6?
Given that ;
Maximum number of cars sold on a day $$=12$$
Minimum numbers of cars sold in a day $$\ge2$$
To determine whether the average number of cars sold during the week was >6
Total numbers of car sold during the week =6*7=42
Now, we have to find out if the average numbers of cars sold during the week =42 or not

Statement 1= During that week, the second smallest number of cars sold on any one day was 4
it can be 2,4,5,5,5,5,12 =38 which is less than 42
There is also another possibility of 2,4,10,10,10,10,12 =58 which is greater than 42, hence
Statement 1 is INSUFFICIENT.

statement 2= During that week the median number of cars sold was 10.
Minimum number of cars sold=2
Maximum numbers of cars sold =12
Median =10

2,2,2,10,10,10,12 =48 This is greater than 42 and it is the smallest possible occurrence for the statement hence statement 2 is SUFFICIENT

$$answer\ is\ option\ B$$
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