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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There are 10 employees in an office. The table shows how
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Gmat_mission
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B
C
D
E
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List of 10 pet values implied by the chart: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
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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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: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
(0 * 2 + 1 * 3 + 2 * 2 + 3 * 3 + x)/11 = 2
16 + x = 22
x = 6
Answer: D
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