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

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Bunuel
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The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   01 May 2018, 05:42
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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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E
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chetan2u
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   26 Sep 2018, 07:40
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Bunuel wrote:
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


Hi stne
First quartile means the lower 25%..
So divide 80 in descending order..
20+20+20+20
Now mark is at 20+20+20+2=62 position from top or 80-62+1=19th from bottom

8 more join at bottom...
So total 88.. and mark moves to 19+8=27th position from bottom

Now the quartiles change..
The first quartile becomes of 88/4=22 persons..
So mark is 27th and not in first quartile but moves to second quartile..
He will be 27-22=5th from bottom in second quartile..

E
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   01 May 2018, 06:46
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Bunuel wrote:
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


Initial divide: \(20-20-20-20\)
New divide: \(22-22-22-22\)

Initially Mark was \(19\)th. This means, \(18\) people got lower salary than Mark. After adding \(8\) people to the first quartile, to make it \(22\), we have to add \(14\) people from initial first quartile.

Now \(18-14=4\) people who got lower salary than Mark are in the second quartile.

Hence, Mark gets the fifth-lowest salary in the second quartile.

Answer: E
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   26 Sep 2018, 06:52
Tulkin987 wrote:
Bunuel wrote:
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


Initial divide: \(20-20-20-20\)
New divide: \(22-22-22-22\)

Initially Mark was \(19\)th. This means, \(18\) people got lower salary than Mark. After adding \(8\) people to the first quartile, to make it \(22\), we have to add \(14\) people from initial first quartile.

Now \(18-14=4\) people who got lower salary than Mark are in the second quartile.

Hence, Mark gets the fifth-lowest salary in the second quartile.

Answer: E


Hi chetan2u,
This solution is not very clear , can you help with this.
Where in the question does it say that the 8 new people were added to the first quartile?
By quartile I assume we mean quarter?
when we are dividing the people into quarters do we first arrange them in ascending order of their salaries,i.e. all the people in First quarter have salaries greater than all the people in second quarter?
Thank you.
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   09 Aug 2020, 10:33
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Bunuel wrote:
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


Solution:

Since there are 80 employees, each quartile contains 80/4 = 20 employees. In particular, the first quartile contains 20 employees with the lowest salaries. Since Mark’s salary is the second-highest salary in the first quartile, his salary is the 19th lowest salary.

If 8 new employees were hired, each quartile would contain 88/4 = 22 employees. Since all of their salaries would be less than the lowest of the 80 salaries, there would be 8 employees with the lowest salaries, and this would push Mark’s salary to be the 27th lowest salary of the 88 employees, or the fifth lowest salary in the second quartile.

Answer: E
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink] New post   26 Jul 2023, 07:46
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Re: The company at which Mark is employed has 80 employees, each of whom [#permalink]
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