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# In a company, 58% of all its employees earn lesser than \$50,000; 66%

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Current Student
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
In a company, 58% of all its employees earn lesser than \$50,000; 66%  [#permalink]

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08 Sep 2014, 02:04
3
7
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:48) correct 31% (03:04) wrong based on 138 sessions

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In a company, 58% of all its employees earn lesser than \$50,000; 66% earn more than \$40,000; 17% earn \$45,000; 3% earn \$48,000. What is the median salary

A) 42,000
B) 43,000
C) 44,000
D) 45,000
E) 46,000

Source: 4gmat

Our instructor told us that this was a 750+ GMAT question

Can someone help me solve this problem
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: In a company, 58% of all its employees earn lesser than \$50,000; 66%  [#permalink]

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08 Sep 2014, 21:59
4
3
alphonsa wrote:
In a company, 58% of all its employees earn lesser than \$50,000; 66% earn more than \$40,000; 17% earn \$45,000; 3% earn \$48,000.
What is the median salary

A) 42,000
B) 43,000
C) 44,000
D) 45,000
E) 46,000

Source: 4gmat

Our instructor told us that this was a 750+ GMAT question

Can someone help me solve this problem

58% of all its employees earn lesser than \$50,000 --> so 42% earn 50k or more
66% earn more than \$40,000 --> so 34% earn 40k or less

................40k..............................45k.....................48k..................50k.............................
....(34%).......................................(17%)...................(3%)..................................(42%).......

34%+42% = 76% earn less than 40k or more than 50k so 24% lie between them.
Out of 24%, 17% earn exactly 45k and 3% earn exactly 48k so other 4% lie somewhere between 40k and 50k but not at 45k or 48k.
To get the median, we need the salaries where 50% and 51% lie.
If the 4% lie between 40k and 45k, the 50% and 51% will lie on 45k.

................40k..............................45k.....................48k..................50k.............................
....(34%)....................(4%).............(17%)...................(3%)..................................(42%).......

The highlighted portion includes 50% as well as 51%.

If the 4% lie beyond 45k, still the 50% and 51% will lie on 45k.

................40k..............................45k.....................48k..................50k.............................
....(34%).......................................(17%)......(4%)......(3%)..................................(42%).......

The highlighted portion includes 50% as well as 51%.

So in any case, answer will be that median salary lies at 45,000.

Note: The lazy genius will mark 45k immediately and move on without doing any of the above - notice why:
No data is available about any of the other options. If I know that x% people lie between 40k and 50k, they could very well all be at 41k or all could be at 49k. No one data point stands out. For median, we need a single data point and hence, to get an exact answer - which is a must in a PS question - the median must lie at 45k.
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Re: In a company, 58% of all its employees earn lesser than \$50,000; 66%  [#permalink]

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08 Sep 2014, 08:12
This is similiar to the posted by netcaesar

But here we need to consider 200 as the no of employees.
58% earn less than 50,000 ===> 116 employees ( 1- 116 - in sequence) earn less than 50,000.
66% earn greater than 40,000 ====> 132 employees ( 69- 200 - in sequence) earn greater than 40,000.

Interfacing range is 69 - 116 earn in the range of 40k to 50k. that is 48 employees in this range.
Median will be average of 100th and 101th employee salary

next info -
17% earn 45000 - that is 34 employees
3% earn 48000 that is 6 employees.
So we know 40 employees salary in the range of 40k to 50 k. 8 employee salary is unknown.

Conclusion:
if 69 employee earn 45000, till 102 employee salary will be 45000. then 100 and 101 employee will also earn 45000. Hence median will be 45,000.
worst case, If 8 unknown employee earn between 40k to 45k, then 69 - 76th employee will earn in this range. then 77th to 112 will earn 45,000. In this case also 100 and 101 employee will earn 45,000. Hence median will be 45,000.
Intern
Joined: 31 May 2013
Posts: 11
Re: In a company, 58% of all its employees earn lesser than \$50,000; 66%  [#permalink]

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08 Sep 2014, 10:06
as only amount mentioned in the question and in the options is \$45000 (\$48000 not mentioned)
and we are only sure of this Salary amount .being present
Rest amounts are in the form of greater than or lesser than , Hence C \$45000
Director
Joined: 09 Aug 2017
Posts: 500
Re: In a company, 58% of all its employees earn lesser than \$50,000; 66%  [#permalink]

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22 Jan 2019, 15:56
This is the way how I did it.
58% of all its employees earn lesser than \$50,000; 66% earn more than \$40,000; 17% earn \$45,000; 3% earn \$48,000.
Median salary=?
58% of all its employees earn lesser than \$50,000; 66% earn more than \$40,000;
From this I inferred that 24% are between \$40000-\$50000. Therefore, 42% earn more than \$50000
and 34% earn less than \$40000.
Now 17%- 45000
and 3%- 48000
Now I ordered % of employees in terms of increasing salary
34% 3% 17% 3% 42%
<\$40K B/W \$40K-\$45K \$45K \$48K >\$50K
Now I can say median salary is 45K.

I hope my understanding to question is correct.
I deserve kudos.
Re: In a company, 58% of all its employees earn lesser than \$50,000; 66%   [#permalink] 22 Jan 2019, 15:56
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