PSAT Math Multiple-Choice Question 394: Answer and Explanation

Question: 394

Year	Number of Eligible Employees
2010	n
2011	874
2012	795
2013	732
2014	821

The table above shows the number of employees at a certain company who were eligible for group health insurance each year from 2010 to 2014. If the median number of eligible employees for the five years was 821, and no two years had the same number of eligible employees, what is the least possible value for n ?

• A. 733
• B. 796
• C. 822
• D. 875

Correct Answer: C

Explanation:

C

Difficulty: Hard

Getting to the Answer: The median is the middle number in a series of numbers. Arrange the number of employees from least to greatest, making sure that 821 is in the middle. Use n to balance out the number of eligible employees on either side of 821:

732, 795, 821, 874, n

or

732, 795, 821, n, 874

Because there are two numbers below the median (732 and 795), there must be two numbers above the median, 874 and n. Be careful—n could be on either side of 874. Since no two years had the same number, n could be anything greater than 821. Its least possible value is 822. Choice (C) is correct.