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The company at which Mark is employed has 80 employees, each

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The company at which Mark is employed has 80 employees, each [#permalink] New post 18 Jan 2016, 15:48
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Question Stats:

76% (01:06) correct 23% (02:22) wrong based on 17 sessions
The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark’s salary of $43,700 is the second-highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark’s salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries?

 A The fourth-highest salary in the first quartile
 B The highest salary in the first quartile
 C The second-lowest salary in the second quartile
 D The third-lowest salary in the second quartile
 E The fifth-lowest salary in the second quartile

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Question: 13
Page: 341
Difficulty: hard
[Reveal] Spoiler: OA

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Re: The company at which Mark is employed has 80 employees, each [#permalink] New post 18 Jan 2016, 15:55
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Solution

In this question you are told that Mark’s salary is the second-highest in the first quartile. From this you can conclude that the word quartile refers to one of the four groups that are created by listing the data in increasing order and then dividing the data into four groups of equal size. When the salaries of the 80 employees are listed in order, the 20 lowest salaries (that is, the salaries in the first quartile) are the first 20 salaries in the list. Since Mark’s salary is the second-highest in the first quartile, 18 salaries in that quartile are lower than his, and one salary in that quartile is higher than his. After the salaries of the 8 new employees are added, there are 26 salaries that are lower than Mark’s. The lowest 22 of those would be in the first quartile of the 88 salaries, and the remaining 4 (salaries 23 to 26) would be in the second quartile, followed by Mark’s salary. This puts Mark at the fifth-lowest salary in the second quartile.

The correct answer is \(E.\)

Alternative Solution

Another way to approach this problem is to think of all 80 salaries numbered in order from least to greatest, the lowest salary at the number 1 position and the greatest salary at the number 80 position. There are 20 positions in each quartile, and Mark’s salary is at position 19. The diagram below shows the salary positions and the quartile into which each position falls. Note that position 19, where Mark’s salary appears, is second-highest in the first quartile.

Image

To see what Mark’s position is with respect to the quartiles of the 88 salaries, you need add the 8 new salaries to the list, renumber the list from 1 to 88, and put 22 salaries in each quartile. Because the 8 new salaries are less than the original 80 salaries, they must be listed in positions 1 through 8, and all salaries in the original list must move up by 8 positions in the renumbered list. In particular, Mark’s salary moves from position 19 to position 27. The diagram below shows the renumbered list. Note that Mark’s salary is in position 27, the fifth position in the second quartile.

Image

Since Mark’s salary is in the fifth position in the second quartile and the salaries are listed in order from least to greatest, Mark’s salary would be the fifth-lowest in the second quartile.
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Re: The company at which Mark is employed has 80 employees, each [#permalink] New post 08 Jan 2017, 11:50
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2nd approach is great
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Re: The company at which Mark is employed has 80 employees, each [#permalink] New post 16 Jan 2017, 19:57
 D The third-lowest salary in the second quartile
Re: The company at which Mark is employed has 80 employees, each   [#permalink] 16 Jan 2017, 19:57
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