Each of the n employees at a certain company has a different annual sa

Question

Each of the n employees at a certain company has a different annual salary. What is the median of the annual salaries of the n employees?

(1) When the annual salaries of the n employees are listed in increasing order, the median is the 15th salary.
(2) The sum of the annual salaries of the n employees is $913,500.

(DS00254)

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • Each of the n employees at a certain company has a different annual salary

To find:  
 • The median of the annual salaries of the n employees

Analysing Statement 1  
 • As per the information given in statement 1, when the annual salaries of the n employees are listed in increasing order, the median is the 15th salary.
 o From this we can only say that there are 14 + 1 + 14 = 29 employees in the company, or n = 29
o But from this statement, we cannot find out any specific value of the median salary, which is the salary of the 15th employee, in increasing order

Hence, statement 1 is not sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, the sum of the annual salaries of the n employees is $913,500
 o From this we cannot find any information about the median salary, as we don’t have any data about the individual salaries of the n employees

Hence, statement 2 is not sufficient to answer

Combining Both Statements  
Combining the information from both the statements, we can write:
 • The median salary is the 15th salary – hence total number of employees will be 29
• The sum of the annual salaries of all the employees is $913,500
 o From this, we can find out the mean salaries of all the employees but not necessarily the median

Hence, the correct answer is option E.

Answer: E

energetics · Answer

One thing to note is that the answer would be C if the problem was changed to state "Each of the n employees at a certain company has  the same  annual salary."

Then, combining the statements we could find the salary since median would equal mean.

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=KtEMMydYK-c

gmatzpractice · Answer

IMO E
Is there a different "style" to the additional 2019 questions? I don't have the book.

BrentGMATPrepNow · Answer

Anyone else notice how many of the new quant questions are related to Medians? 
 
Seems almost excessive.

Cheers,
Brent

ShashwatPrakash · Answer

We need to find the value of the median salary.

St 1: The median is the 15th salary, so we can say company has 14 + 1 + 14 = 29 employees or n = 29. 
We don't get any value for the median salary - Insufficient

St 2: the sum of the annual salaries of the n employees is $913,500
No information about the median salary, as we don’t have any information about the individual salaries.

Combine, we don't get any value for the median salary. Hence OA (E)

NA_JS · Answer

This is one of the most interesting questions. The answer could have been C if it were mentioned that either a)salary is same or b) the salary is in AP for all the employees

09173140521 · Answer

maybe GMAT like median !....2 days ago I go for prep official and see 2-3 out of 31 is related to median.
I saw 2-3 new question in og 2020 median

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=WQwS2_hqYgQ

ScottTargetTestPrep · Answer

Solution:
 
 Question Stem Analysis:

We need to determine the median of the annual salaries of the n employees at a certain company.

Statement One Alone:

Since we know the median salary is the 15th highest salary, we can determine that the value of n is 29. That is, there are 29 employees in the company. However, we can’t determine the median of the annual salaries of the 29 employees. Statement one alone is not sufficient.
 
 Statement Two Alone:
 
Knowing the sum of the annual salaries does not allow the median of the annual salaries of the n employees to be discerned. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we can determine the average (or arithmetic mean) annual salary of the 29 employees. However, we still can’t determine the median annual salary since the mean and the median of a set of numbers are not necessarily the same value. Both statements together are not sufficient. 
 
 Answer: E

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Each of the n employees at a certain company has a different annual sa

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