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## The numbers of cars sold at a certain dealership

This topic has 3 expert replies and 1 member reply
boomgoesthegmat Senior | Next Rank: 100 Posts
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#### The numbers of cars sold at a certain dealership

Mon Apr 25, 2016 2:41 pm
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 number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II, and III

### Top Member

swerve Master | Next Rank: 500 Posts
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Thu Mar 15, 2018 10:13 am
Hi boomgoesthegmat,

Here is my way to solve this question,

If we arrange the numbers in ascending order 2, 3, 4, x, 6, 7, 8, &, observe closely it is an evenly spaced series with one missing number. For an evenly spaced series mean is equal to the median. Thus to fulfill the condition of mean = median, x has to be 5 only.

Regards!

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
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Thu Mar 15, 2018 9:29 am
boomgoesthegmat wrote:
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 number of cars sold per day for the seven days?

I. 2
II. 4
III. 5

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II, and III
To solve, we will use the number given in each Roman numeral to determine the average and median and determine whether they are equal.

I. 2

In order, from least to greatest, our values for the number of cars sold for the 7 days are:

2, 2, 3, 4, 6, 7, 8

We know that the median is the middle number of our list, so our median is 4. Next we calculate the average.

Average = sum/quantity

Average = (2 + 2 + 3 + 4 + 6 + 7 + 8)/7

Average = 32/7

We see that the average does not equal the median.

Answer choice I is not correct. We can eliminate answer choices C and E.

II. 4

In order, from least to greatest, our values for the number of cars sold for the 7 days are:

2, 3, 4, 4, 6, 7, 8

We know that the median is the middle number of our list, so our median is 4. Next we calculate the average.

Average = sum/quantity

Average = (2 + 3 + 4 + 4 + 6 + 7 + 8)/7

Average = 34/7

We see that the average does not equal the median.

Answer choice II is not correct. We can eliminate answer choices A and D. We know now that the correct answer choice is B, but we should still check.

III. 5

In order, from least to greatest, our values for the number of cars sold for the 7 days are:

2, 3, 4, 5, 6, 7, 8

We know that the median is the middle number of our list, so our median is 5. Next we calculate the average.

Average = sum/quantity

Average = (2 + 3 + 4 + 5 + 6 + 7 + 8)/7

Average = 35/7 = 5

We can see that the average does equal the median.

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Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Apr 25, 2016 3:43 pm
Hi boomgoesthegmat,

This question is essentially a big 'concept' question with a little bit of math thrown in. We're asked which of the 3 Roman Numerals would give us a situation in which the average of the group would equal the median of the group.

Since we're dealing with a group of 7 numbers (the 6 that we're given and the 7th that is either 2, 4 or 5), the median will be the 4th number (once the values are put in ascending order).

The total number of cars sold in 6 days is 4+7+2+8+3+6=30.
In order, those numbers are 2, 3, 4, 6, 7, 8 ...and X, although we don't know what X is yet.

Since the median will be an integer, we need to add a number to the group that, when the sum of the group is divided by 7, gives us an integer also AND that integer has to match the median.

Looking at the 3 Roman Numerals, there's only one that fits everything we're looking for: 5

(30+5)/7 = 5 --> 5 is the average
2, 3, 4, 5, 6, 7, 8 --> 5 is the median

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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Matt@VeritasPrep GMAT Instructor
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Wed Apr 27, 2016 2:14 pm
We know the mean is

(4 + 7 + 2 + 8 + 3 + 6 + x) / 7, or (30 + x)/7

The set has an odd number of terms, so the median will be an integer.

That means that (30 + x)/7 must ALSO be an integer. For our three options, this will only work if x = 5, so III is the only possibility.

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