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

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

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New post 08 Sep 2014, 02:04
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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
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Re: In a company, 58% of all its employees earn lesser than $50,000; 66%  [#permalink]

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New post 08 Sep 2014, 21:59
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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


A diagram will help you see it quickly:

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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New post 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.
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Re: In a company, 58% of all its employees earn lesser than $50,000; 66%  [#permalink]

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New post 08 Sep 2014, 10:06
i made a guess
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
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Re: In a company, 58% of all its employees earn lesser than $50,000; 66%  [#permalink]

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New post 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.
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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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