Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 271

There are 10 employees in an office. The table shows how man
[#permalink]
Show Tags
17 Nov 2010, 12:57
Question Stats:
71% (02:47) correct 29% (02:38) wrong based on 271 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 22 33 A. 3 B. 4 C. 5 D. 6 E. 7 Edit: Formatting
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
I'm the Dumbest of All !!




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: There are 10 employees in an office. The table shows how man
[#permalink]
Show Tags
17 Nov 2010, 13:16
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 22 33
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). Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 271

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: 112

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 7695 times ]



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: There are 10 employees in an office. The table shows how man
[#permalink]
Show Tags
13 Sep 2013, 13:20



SVP
Joined: 06 Sep 2013
Posts: 1764
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: 2657
Location: United States (IL)
Concentration: Finance, Economics
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 multivoting 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: 6970

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 multivoting 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 250100 voted for B only.. ans C 150
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)

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. 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
CoFounder & 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 &nbs
[#permalink]
14 Mar 2018, 20:20






