GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jan 2019, 18:26

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431
The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

06 Aug 2012, 01:43
3
20
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:59) correct 11% (02:05) wrong based on 2001 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

06 Aug 2012, 01:43
9
8
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).

_________________
Senior Manager
Joined: 24 Aug 2009
Posts: 469
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

19 Aug 2012, 13:39
23
6
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

##### General Discussion
Manager
Joined: 28 Sep 2011
Posts: 60
Location: United States
GMAT 1: 520 Q34 V27
GMAT 3: 690 Q47 V38
GPA: 3.01
WE: Information Technology (Commercial Banking)
Re: The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

06 Aug 2012, 12:31
1

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.
Manager
Joined: 07 Apr 2014
Posts: 111
Re: The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

09 Sep 2014, 21:44
2
Bunuel 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

Practice Questions
Question: 12
Page: 153
Difficulty: 600

if the reading part is done carefully, then we could get the solution in 30 secs.

2+3+4+6+7+8 = 30 so if u add 2 then mean= 32/7 not equal to 4(median).
if 4 then 34/7 not equal to median (4).
if % then 35/7 equal to median 5. set will be like [2,3,4,5,6,7,8,]..

Intern
Joined: 23 Mar 2016
Posts: 29
Schools: Tulane '18 (M$) Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 28 Apr 2016, 19:32 1 This is fairly simple, you don't have to do much work. First, add up the numbers in your head (30), look at the 1,2,3 choices, and realize only 5 will be divisible by 7. you don't even need to arrange the numbers around to figure the median. time saver for the win Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 29 Apr 2016, 08:28 1 1 Bunuel 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 Practice Questions Question: 12 Page: 153 Difficulty: 600 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. Answer choice III is correct. The answer is B. _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 25 Jun 2015 Posts: 8 Location: Portugal GMAT 1: 370 Q37 V37 GPA: 2.92 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 22 Jul 2016, 04:19 I think the easiest way would be the smallest number (2) + the biggest number (8) = 10/2 = 5 Current Student Joined: 12 Aug 2015 Posts: 2626 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 26 Dec 2016, 00:26 2 Nice Question. Here is what i did in this one -> Mean=30+x/7 = Median Since #=7 => Median will be in the series. Hence median must be an integer. So 30+x must be divisible by 7 Only 5 out of 2,4,5 will make that possible . Hence only 5 Hence B _________________ MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs! STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+) AVERAGE GRE Scores At The Top Business Schools! Director Joined: 02 Sep 2016 Posts: 678 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 01 Apr 2017, 08:09 1 When the numbers are consecutive integers, then the mean of the set is equal to the median. (This is one case where median= mean) Here median will be the 4th integer in the set (after arranging the values in ascending/descending order). Therefore the answer is 5. _________________ Help me make my explanation better by providing a logical feedback. If you liked the post, HIT KUDOS !! Don't quit.............Do it. Current Student Joined: 18 Jun 2016 Posts: 264 Location: India GMAT 1: 720 Q50 V38 GMAT 2: 750 Q49 V42 GPA: 4 WE: General Management (Other) Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 22 Jun 2017, 04:05 1 1 Bunuel 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 Practice Questions Question: 12 Page: 153 Difficulty: 600 Fastest way to solve a Roman Numeral Question - 1. DO NOT START WITH THE 1st ROMAN NUMERAL. Check the most occurring roman numeral in the 5 options and check for it first. Here it is II, occurring in 4 options. Checked. Did not work. Answer is B. _________________ I'd appreciate learning about the grammatical errors in my posts Please hit Kudos If my Solution helps My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html Manager Joined: 19 Jul 2017 Posts: 85 Location: India Concentration: General Management, Strategy GPA: 3.5 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 25 Aug 2017, 08:19 Bunuel wrote: 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. Perfect . This makes sense ! My approach was to find the mean and average by substituting the 3 numbers given. But this one saves time Study Buddy Forum Moderator Joined: 04 Sep 2016 Posts: 1299 Location: India WE: Engineering (Other) The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 12 Sep 2017, 19:14 Bunuel niks18 amanvermagmat Quote: 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. I hope you simply mean to convey that median needs to be an integers since it represents no of cars and hence it can not be a fraction. Eg. no of children / umbrella can not be fraction. If i look closely the nos are evenly spaced, can I not conclude directly 5 as mean since all consecutive no shall pull mean in same sequence. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13377 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The numbers of cars sold at a certain dealership on six of [#permalink] ### Show Tags 04 Feb 2018, 11:34 Hi All, 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 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

04 Feb 2018, 18:35
Bunuel niks18 amanvermagmat
Quote:
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.

I hope you simply mean to convey that median needs to be an integers since it represents no of cars and hence it can not be a fraction.

Eg. no of children / umbrella can not be fraction.

If i look closely the nos are evenly spaced, can I not conclude directly 5 as mean since all consecutive no
shall pull mean in same sequence.

Yes we have a consecutive series if 5 is included. So mean=median

Posted from my mobile device
Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

05 Feb 2018, 00:08
Bunuel 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

Practice Questions
Question: 12
Page: 153
Difficulty: 600

In an AP with odd number of terms, the Median is always equal to the Middle Number.
I we arrange the numbers in ascending order, we have -
$$2,3,4,a,6,7,8.$$
Here, a can be only 5.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Intern
Joined: 01 May 2017
Posts: 36
The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

Updated on: 07 Apr 2018, 06:58
1
In questions involving answer choices, which contain various combinations of three roman numerals, following technique is generally very helpful:

1 - See which of the roman numeral options is occuring the most in the five answer choices

2 - Guess that roman numeral option as the right answer and check it against the question by using the relavent technique such as back solving, and algebra etc.

3 - If the anwer is incorrect then remove all the answer choices, which contain that roman numeral

4 - repeat 1, 2, and 3 until you are down to only one answer choice

In this question, the most occuring roman numeral is II, which is found in four of the five choices.

Remember: if this question were a 650+ question then there would have been no more than two answer choices with the same roman numeral; but since this is a relatively easier question, so we see that by just guessing and checking on one roman numeral option i.e. II, we are left with single answer choice (B), which is the answer!

Solving for roman numeral option (II):
Median: 4
Average: 34/7 is greater than 4
So 4 cannot be the 7th value

Originally posted by FANewJersey on 07 Apr 2018, 06:53.
Last edited by FANewJersey on 07 Apr 2018, 06:58, edited 1 time in total.
Intern
Joined: 01 May 2017
Posts: 36
The numbers of cars sold at a certain dealership on six of  [#permalink]

### Show Tags

07 Apr 2018, 06:54
rahul16singh28 wrote:
Bunuel 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

Practice Questions
Question: 12
Page: 153
Difficulty: 600

In an AP with odd number of terms, the Median is always equal to the Middle Number.
I we arrange the numbers in ascending order, we have -
$$2,3,4,a,6,7,8.$$
Here, a can be only 5.

rahul16singh28 Not necessarily, "a" could also be 4. Kindly recheck your logic.
The numbers of cars sold at a certain dealership on six of &nbs [#permalink] 07 Apr 2018, 06:54
Display posts from previous: Sort by