• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

## The numbers of cars sold at a certain dealership

This topic has 2 expert replies and 0 member replies
boomgoesthegmat Senior | Next Rank: 100 Posts
Joined
25 Apr 2016
Posted:
93 messages
1

#### 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

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
625
Target GMAT Score:
V51
GMAT Score:
780
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.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
8946 messages
Followed by:
468 members
2867
GMAT Score:
800
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

_________________
Contact Rich at Rich.C@empowergmat.com

### Best Conversation Starters

1 lheiannie07 112 topics
2 swerve 64 topics
3 LUANDATO 64 topics
4 ardz24 61 topics
5 AAPL 57 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

227 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

176 posts
3 Jeff@TargetTestPrep

Target Test Prep

168 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

138 posts
5 GMATGuruNY

The Princeton Review Teacher

129 posts
See More Top Beat The GMAT Experts