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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

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

by Gmat_mission » Wed Apr 17, 2019 1:29 am

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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

[spoiler]OA=D[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Wed Apr 17, 2019 1:29 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 17, 2019 3:20 am

Gmat_mission 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

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

List of 10 pet values implied by the chart:
0, 0, 1, 1, 1, 2, 2, 3, 3, 3

Since the answer choices are all 3 or greater, the addition of the manager's pet value will yield the following list of 11 values:
0, 0, 1, 1, 1, 2, 2, 3, 3, 3, M

Since the new average must be equal to the median value in blue, the sum of the 11 values = (count)(average) = 11*2 = 22.
Thus:
0+0+1+1+1+2+2+3+3+3+M = 22
16+M = 22
M = 6

The correct answer is D.

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by Scott@TargetTestPrep » Mon May 06, 2019 7:14 pm

Gmat_mission 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

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

[spoiler]OA=D[/spoiler]

Source: Magoosh

Let x = the number of pets the manager has. If x is 1 or less, then the median is 1. If x is 2 or more, then the median is 2. From the given choices, we can expect that x is 2 or more, therefore, we have:

(0 * 2 + 1 * 3 + 2 * 2 + 3 * 3 + x)/11 = 2

16 + x = 22

x = 6

Answer: D

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