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

 It is currently 16 Jul 2018, 11:39

### 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

# There are 10 employees in an office. The table shows how man

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 288
There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

17 Nov 2010, 12:57
6
00:00

Difficulty:

65% (hard)

Question Stats:

68% (02:01) correct 32% (01:52) wrong based on 265 sessions

### HideShow timer Statistics

There are 10 employees in an office. The table shows how many employees have 0, 1, 2 or 3 pets. If the office manager were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?

# of pets # of employees
0 ---------------2
1-------- ------3
2--------------2
3--------------3

A. 3
B. 4
C. 5
D. 6
E. 7

Edit: Formatting

_________________

I'm the Dumbest of All !!

Math Expert
Joined: 02 Sep 2009
Posts: 47018
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

17 Nov 2010, 13:16
2
3
shrive555 wrote:
There are 10 employees in an office. The table shows how many employees have 0, 1, 2 or 3 pets. If the office manager were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?

# of pets # of employees
0 ---------------2
1-------- ------3
2--------------2
3--------------3

3
4
5
6
7

So we have the following set {0, 0, 1, 1, 1, 2, 2, 3, 3, 3, x}, 11 terms represent 11 employees (including office manager) and x represents the number of pets office manager has.

Now, $$mean=\frac{0+0+1+1+1+2+2+3+3+3+x}{11}=\frac{16+x}{11}$$ and $$median=6_{th} \ term$$ (median equals to the middle term in the set with odd number of terms when arranged in ascending or descending order), so in ANY case it must be an integer --> as given that mean=median, then $$mean=\frac{16+x}{11}$$ must be an integer --> $$x=6$$ (in this case $$mean=\frac{16+x}{11}=2$$ and median= 6th term = 2 also).

_________________
##### General Discussion
Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 288
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

17 Nov 2010, 13:27
Thanks alot B.
B why Arithmetic Mean isn't included in the gmat math book ? isn't any thread that gives insight/tips/pitfalls on Mean/average
_________________

I'm the Dumbest of All !!

Manager
Joined: 16 Jul 2010
Posts: 128
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

18 Nov 2010, 07:28
Quite straightforward if you know your formulas. Took me some time to solve. I think I need to practice more. Thanks for the question!
Intern
Joined: 28 May 2013
Posts: 13
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

13 Sep 2013, 13:17
There are 10 employees in an office, not counting the office manager. The table shows how many employees have 0, 1, 2 or 3 pets. If the office manager also were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?

a) 3
b) 4
c) 5
d) 6
e) 7
Attachments

pets_q.png [ 11.05 KiB | Viewed 7013 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 47018
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

13 Sep 2013, 13:20
AkshayChittoria wrote:
There are 10 employees in an office, not counting the office manager. The table shows how many employees have 0, 1, 2 or 3 pets. If the office manager also were included in the table, the average (arithmetic mean) number of pets per person would equal the median number of pets per person. How many pets does the office manager have?

a) 3
b) 4
c) 5
d) 6
e) 7

Merging similar topics.
_________________
SVP
Joined: 06 Sep 2013
Posts: 1869
Concentration: Finance
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

10 Feb 2014, 13:47
This one's pretty easy because the mean 16+x/11 is an integer only when x = 6. And since we have an odd number of members then the median is always an integer, given that all terms in the given set are integers. Therefore, only D works

Hope its clear
J
Board of Directors
Joined: 17 Jul 2014
Posts: 2726
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

09 Jan 2016, 12:02
let's list everything:
0 0 1 1 1 2 2 3 3 3
ok, so if we add new number, then the median would be either 1 or 2.
the total sum is 3+4+9=16.
new number = x.

16+x/11 = either 1 or 2.
16+x=11 - impossible to be negative, thus, the median, and the average has to be 2.
16+x/11=2 -> 16+x=22 -> x=6.

took me slightly over 1 minute to answer.

D.
Intern
Joined: 16 Nov 2015
Posts: 17
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

12 Feb 2016, 19:38
In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Math Expert
Joined: 02 Aug 2009
Posts: 6210
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

12 Feb 2016, 20:09
leve wrote:
In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250

Hi leve,
you should have posted the Q separately..
otherwise..
100 voters voted for A...
50 voted for both A and B, but this is already a part of 100 above..
each of 250 voted for A or B..
so remaining 250-100 voted for B only..
ans C 150

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11970
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: There are 10 employees in an office. The table shows how man [#permalink]

### Show Tags

14 Mar 2018, 20:20
Hi All,

From the table, we know that there are 10 people and 16 pets. By including the manager, we'll have 11 people, so the median will be the 6th number in line and will be an INTEGER.

We're told that once the manager's pets are included, the AVERAGE number of pets will EQUAL the MEDIAN number of pets. This significantly limits the possibilities, since the average will have to be an INTEGER as well.

X = number of manager's pets

Average = (16 + X)/11 = integer

Since we can't have a negative number of pets, X could be 6, 17, 26, etc. With the given answer choices, the only match is 6. Once you include that value, you'll see that both the average and the median are 2.

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!***********************

Re: There are 10 employees in an office. The table shows how man   [#permalink] 14 Mar 2018, 20:20
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.