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Company A has a total of n employees, where n is an odd integer, and n

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Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   Updated on: 23 May 2017, 00:39
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Company A has a total of n employees, where n is an odd integer, and no two employees have the same annual salary. The annual salaries of the n employees are listed in increasing order, and the 16th salary in the list is the median of the annual salaries. If the sum of the annual salaries of Company A’s employees is $942,400, what is the average (arithmetic mean) of the annual salaries of Company A’s employees?

A. $29,450
B. $30,400
C. $32,500
D. $47,120
E. $58,900
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B

Originally posted by michaelkalend on 23 May 2017, 00:36.
Last edited by Bunuel on 23 May 2017, 00:39, edited 1 time in total.
Edited the question.
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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   23 May 2017, 01:18
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michaelkalend wrote:
Company A has a total of n employees, where n is an odd integer, and no two employees have the same annual salary. The annual salaries of the n employees are listed in increasing order, and the 16th salary in the list is the median of the annual salaries. If the sum of the annual salaries of Company A’s employees is $942,400, what is the average (arithmetic mean) of the annual salaries of Company A’s employees?

A. $29,450
B. $30,400
C. $32,500
D. $47,120
E. $58,900


Given that n is odd.

For a set with odd number of terms the median is the middle term (when arranged in ascending/descending order). Thus, 16th salary/employee is right in the middle, which implies that there are total of 31 employees.

The average salary = (total salary)/(number of employees) = 942,400/31 = 30,400.

Answer: B.
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Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   23 May 2017, 06:05
michaelkalend wrote:
Company A has a total of n employees, where n is an odd integer, and no two employees have the same annual salary. The annual salaries of the n employees are listed in increasing order, and the 16th salary in the list is the median of the annual salaries. If the sum of the annual salaries of Company A’s employees is $942,400, what is the average (arithmetic mean) of the annual salaries of Company A’s employees?

A. $29,450
B. $30,400
C. $32,500
D. $47,120
E. $58,900


Total number of n employee is odd integer.
16th salary in the list is the median of the annual salaries.
Therefore there are 15 employee before and after 16th. Total = 15 + 15 + 1 = 31
Sum of the annual salaries of Company A’s employees is = $942,400
Average = \(\frac{942,400}{31}\) = $30,400
Answer B...
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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   23 May 2017, 06:36
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michaelkalend wrote:
Company A has a total of n employees, where n is an odd integer, and no two employees have the same annual salary. The annual salaries of the n employees are listed in increasing order, and the 16th salary in the list is the median of the annual salaries. If the sum of the annual salaries of Company A’s employees is $942,400, what is the average (arithmetic mean) of the annual salaries of Company A’s employees?

A. $29,450
B. $30,400
C. $32,500
D. $47,120
E. $58,900


for all terms to be different the median will be one of the terms only if the number of terms in the set is odd

Median = 16th term i.e. total number of terms = 15+1+15 = 31

Average = Sum / Number of terms = 942,400/31 = 30400

Answer: Opton B
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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   26 May 2018, 09:34
Since the number of employees is an odd number, and median is the 16th salary, we know that mean = median = the middle number.

This shows that the total number of employees is 31.

Average = Sum/number = 942400/31 = 30400.
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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   26 May 2018, 10:35
ok, so we have odd number of employees and the median of employees is 16 (means 15 people before median and 15 people after the median, or 30+1 median=31. We have sum of their salaryies, which is 942 400. To find average, we divide sum by total number of employees or 942400/31=30 400. So answer is B
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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink] New post   07 Aug 2023, 10:35
Hello from the GMAT Club BumpBot!

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Re: Company A has a total of n employees, where n is an odd integer, and n [#permalink]
07 Aug 2023, 10:35
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