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

Question

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

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

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

Formatting

Bunuel · Accepted Answer

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.

shrive555 · Answer

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

Werewolf · Answer

Quite straightforward if you know your formulas. Took me some time to solve. I think I need to practice more. Thanks for the question!

jlgdr · Answer

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

Hope its clear
J

mvictor · Answer

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.

leve · Answer

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

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

chetan2u · Answer

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

EMPOWERgmatRichC · Answer

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:  D

GMAT assassins aren't born, they're made, 
Rich

MathRevolution · Answer

There is a total of 10 employees and a manager is added. Let the manager is represented by 'm'.

The set is {0, 0, 1, 1, 1, 2, 2, 3, 3, 3, m}

For 11 times, the median will be the number in the sixth position. Also, the inclusion of a manager makes the median = mean.

Mean:  \frac{(0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + m)}{ 11}  = Median

=>  \frac{(m + 16)}{11}  = Median

In order to be  \frac{(m + 16)}{11}  to be an integer 'm' should be 6.

Then Median = 2 and Mean = 2.

Hence, the manager will have 6 pets.

Answer D

bumpbot · Answer

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