Source: Official Guide for GMAT Review 2016 Problem Solving; #10

1

# The numbers of cars sold at a

The numbers of cars sold at a certain dealership on six of the last seven business days were 4, 7, 2, 8, 3, and 6, respectively. If the number of cars sold on the seventh business day was either 2, 4, or 5, for which of the three values does the average (arithmetic mean) number of cars sold per business day for the seven business days equal the median numbers of cars sold per day for the seven days?

### 2 Explanations

1

marina kawai

Dear Mike

question asked for 7 days mean, but you just calculated mean for 6 days,
why?

Jun 4, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Marina!

I'm happy to clarify :) In the explanation, Mike starts off by adding up the values we know for sure--how many cars were sold in the first six days. As he notes, a total of 30 cars were sold in those first six days. At this point, we need to consider the three options for the 7th day separately:

I. 2
II. 4
III. 5

We find the mean of the 7 days by adding each of these values to 30 and then dividing by 7. When we do so, we find that only III. 5 gives us an integer value for the mean of the 7 days (mean = 35/7 = 5).

This helps us because we're asked for the number of cars sold on day 7 which will lead to the mean equaling the median. Since the set has an odd number of terms (7), the median will be one of those seven terms. And because those seven terms are # of cars sold, all of the terms (and therefore the median) will be integers.

So, we can conclude that III. 5 is the only possible number of cars sold on day 7 in the options provided. :)

I hope this clears up your doubts! Mike McGarry, Magoosh Tutor