Data Sufficiency

BTGmoderatorDC wrote: ↑

Tue Jul 03, 2018 5:01 pm

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.

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