Not clear on this median problem

Question

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?

Uva@90 · Answer

Hi Shibriz, It is given that Mean = Median and there are 11 members in total Median => should be an integer. 16+x/11 = mean or median(integer) so, only possible answer is, x = 6 Regards, Uva

Rich.C@EMPOWERgmat.com · Answer

Hi shibsriz,

Uva@90 has correctly answered the question; I'm going to add a few more details into the explanation.

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 = 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.

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Rich

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GMATGuruNY · Answer

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?

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

Answer choices:
3
4
5
6
7

Total number of pets = (number of employees)(average number of pets per employee).
Since the average is equal to the median, we get:
Total number of pets = (number of employees)(median number of pets per employee).

Pet values:
2 employees each have 0 pets --> 0, 0
3 employees each have 1 pet --> 1, 1, 1
2 employees each have 2 pets --> 2, 2
3 employees each have 3 pets --> 3, 3, 3
Manager has x pets --> x.

Since the answer choices are all 3 or greater, the manager must have at least 3 pets.
Listing the pet values in order, we get:
0, 0, 1, 1, 1, 2, 2, 3, 3, 3, x

Since there are 11 employees, and the median number of pets is 2, we get:
Total number of pets = 11*2 = 22.

Thus:
0+0+1+1+1+2+2+3+3+3+x = 22
16+x = 22
x = 6.

The correct answer is D.

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