Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 11:04

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The numbers of cars sold at a certain dealership on six of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24386 [0], given: 2677

The numbers of cars sold at a certain dealership on six of [#permalink] New post 06 Aug 2012, 01:43
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (02:32) correct 19% (01:43) wrong based on 274 sessions
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

Practice Questions
Question: 12
Page: 153
Difficulty: 600
[Reveal] Spoiler: OA

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

6 KUDOS received
Director
Director
avatar
Joined: 24 Aug 2009
Posts: 510
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 9

Kudos [?]: 361 [6] , given: 241

Re: The numbers of cars sold at a certain dealership on six of [#permalink] New post 19 Aug 2012, 13:39
6
This post received
KUDOS
1
This post was
BOOKMARKED
Best Shortcut for this question:-
If we arrange the numbers in ascending order 2,3,4,x,6,7,8,& observe closely it is a evenly spaced series with one missing number. For a evenly spaced series mean is equal to median. Thus to fulfill the condition of mean = median , x has to be 5 only.
It took app 1 min 10 sec for me
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24386 [1] , given: 2677

Re: The numbers of cars sold at a certain dealership on six of [#permalink] New post 06 Aug 2012, 01:43
1
This post received
KUDOS
Expert's post
SOLUTION

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

The median of a set with odd number of elements is the middle element when arranged in ascending/descending order.

Hence, the median number of cars sold for the 7 (odd) days, is the fourth greatest number of cars sold in these 7 days, therefore the median must be an integer.

Next, the total number of cars sold in 6 days is 4+7+2+8+3+6=30.

The average number of cars sold in 7 days is \frac{30+x}{7}. Since we need the average to be equal to the median, then the average must also be an integer.

\frac{30+x}{7}=integer only if x=5 (for x=2 or x=4 it's not an integer).

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 28 Sep 2011
Posts: 67
Location: United States
GMAT 1: 520 Q34 V27
GMAT 2: 550 Q V
GMAT 3: 690 Q47 V38
GPA: 3.01
WE: Information Technology (Commercial Banking)
Followers: 1

Kudos [?]: 14 [0], given: 9

GMAT ToolKit User
Re: The numbers of cars sold at a certain dealership on six of [#permalink] New post 06 Aug 2012, 12:31
[Reveal] Spoiler:
B


Since there are a odd number of days the median will be an integer, if the average has to be equal to median then it must be an integer also. Only 5 does this.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24386 [0], given: 2677

Re: The numbers of cars sold at a certain dealership on six of [#permalink] New post 10 Aug 2012, 02:45
Expert's post
SOLUTION

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

The median of a set with odd number of elements is the middle element when arranged in ascending/descending order.

Hence, the median number of cars sold for the 7 (odd) days, is the fourth greatest number of cars sold in these 7 days, therefore the median must be an integer.

Next, the total number of cars sold in 6 days is 4+7+2+8+3+6=30.

The average number of cars sold in 7 days is \frac{30+x}{7}. Since we need the average to be equal to the median, then the average must also be an integer.

\frac{30+x}{7}=integer only if x=5 (for x=2 or x=4 it's not an integer).

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2073
Followers: 179

Kudos [?]: 35 [0], given: 0

Premium Member
Re: The numbers of cars sold at a certain dealership on six of [#permalink] New post 11 Jan 2014, 22:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The numbers of cars sold at a certain dealership on six of   [#permalink] 11 Jan 2014, 22:47
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic A certain dealership has a number of cars to be sold by its Bunuel 8 27 Dec 2013, 04:37
Q12: A certain dealership has a number of cars to be sold by TriColor 11 17 Jun 2009, 17:36
1 Of the 25 cars sold at a certain dealership yesterday, some sarzan 1 23 Aug 2008, 17:37
Of the 25 cars sold at a certain dealership yestarday, some marcodonzelli 5 28 Dec 2007, 08:29
Of the 25 cars sold at a certain dealership yesterday, some b14kumar 5 09 Sep 2007, 15:25
Display posts from previous: Sort by

The numbers of cars sold at a certain dealership on six of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.