In a company 60% of the employees earn less than $50,000

Question

In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?

A. 43.000
B. 45.500
C. 46.000
D. 49.000
E. 50.000

samark · Accepted Answer

Nice Question!

During my first read, I realized that it is a venn diagram question. So, I solved it this way..

Attachment:

Qus.jpg [ 10.5 KiB | Viewed 15135 times ]

60(<50k) + 60 (>40k) - (Intersection between two categories) = 100

Given Three Categories:
no (I.): Earning < 40k (which amounts to first 40 people). {This is I. only region}
no (II.): Earning between 40 k and 50k (which amounts to 41st to 60 people) {This is Intersection}
no (III.): Earning > 50k (which amounts to 61st to 100th people) {This is III. only region}

We are interested in no (II.) as there are already first 40 people in no (I.).

Also, given : 11 people earn 43k. They can be either 41st to 52nd people or 50th to 60th people. {of course when put in ascending order of their salaries}.

So, In any case..50 and 51 people will be earning 43K. Hence, OA: A.

Bunuel · Answer

Let's consider this problem in the following way: 1. We have set of 100 terms: a1, a2, ..a100. 2. 60 terms are <50 3. 60 terms are >40 4. 11 terms =43 5. 5 terms =49. Q what is median of the set? Clearly as we have even number of terms (100) in the set, the median would be (a50+a51)/2. So we should determine a50 and a51. From 2 and 3 we can conclude that 20 terms: from a41 to a60 are in the range 40-50. Or 40 median=43 Answer: A.

gmate2010 · Answer

In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?

60% of the employees earn less than $50,000 a year
=> 40% earn greater than 50,000 a year.

60% of the employees earn more than $40,000 a year
=> 40% earn less than 40,000 a year..

Let there are 100 employess 
then, to calculate median we need salary of 50th employee and 51th employee.

Then, median = (salary of 50th employee + salary of 51th employee)/2
 40 people<40000 $40,000 20 people $50,000 40 people > 50,000
 --------------------------*----------------*----------------------

Salary of 11 people = 43,000
Salary of 5 people = 49,000
whtever, be the case, 50th and 51th salary would be 43,000 and 43,000

Hence,  median = \frac{(2*43000)}{2}

dolly12 · Answer

Agree A is answer.

50 and 51 employee will be each 43K. hence median = (43K+43k)/2

tejal777 · Answer

Opening this thread again..
Absolutly did'nt grasp the concept guys..Please explain..

In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?

I understood till here..after that it all went above my head:(

prashantbacchewar · Answer

Hi Bunuel,

I am not able to understand this problem

You are saying From 2 and 3 we can conclude that 20 terms: from a41 to a60 are in the range 40-50 how it is so?

Bunuel · Answer

Total 100 terms --> 60(<50)+60(>40()=120 --> 20 overlap in the range 40-50.

prashantbacchewar · Answer

Got it Bunuel.. Thanks a lot

amit2k9 · Answer

good concept used here.

IEsailor · Answer

This is how id did it.

Well the Median should be between the overlap portion of the sets.

Now in this overlap section of 20 % (or say 20 values for the sake of ease) the avg of the 11th and 10th value is the Median of the whole set.

11% earn 43,000
5% earn 49,000
remaining 4%

Now even if these 4% earn less than 43,000( above 40,000) or more than 49,000 ( less than 50,000)
the 10th and the 11th term would still be 43,000

For example

say these 4 values are 
42,000 each
then the set of 20 values would be 
42000 42000 42000 42000 43000 _ _ _ _ 10th Term 11th term _ _ _ _ 49000 49000 49000 49000 49000

Hence under all probabilities the 10th and the 11th term would be 43000 and hence would be the Median of the entire set 
HENCE ANSWER IS A

ufo9038 · Answer

I reasoned like this:

40% over 50
40% less than 40

So we only care about the middle, 40 - 50. To see which one would be in the middle.

From the above, we know that 20% are from 40 to 50. 
Also, 11% are 43

11 is more than half of 20. It means 43 will always appear in the middle, no matter what.

So the median is 43.

hdwnkr · Answer

I used a number line method here.

60 percent make more than 40,000. 
 THis implies, 40 percent make less than 40,000

60 percent make less than 50,000

There is this 20 percent that makes between 40 and 50K and is in the mid 20 percentage, of which 11 percent is 43,000

So, 43,000 is always at the 50th position. Hence, the median

CrackverbalGMAT · Answer

In a company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?

Assume that there are 100 employees in the company.

60 % of the employees i.e 60 % of 100 = 60 employees earn less than $50,000 a year.
Similarly , 60 employees earn more than $40,000 a year.
11 employees earn $43,000 a year.
5 employees earn $49,000 a year.

If we arrange the salaries of the 100 employees in ascending order $S1, S2, S3...........S100$.
Where S1 is the lowest salary paid to the employee and S100 is the highest salary paid to the employee.
The median salary of the company would be average of $(S50 + S51)$ i.e $\frac{(S50 + S51)}{2} $ as the no of employees in the company is even.

Attachment:

median.JPG [ 51.87 KiB | Viewed 7198 times ]

From the above table we can conclude that the salary of S41-S60 lies between $40,000 and $50,000.
Also we need to find S50 and S51 in order to find the median.

Since its given that 11 employees earn $43,000 a year and 5 employees earn $49,000 a year. That means we have the salary details of 16 employees in the range S41-S60. But we are not aware of the salaries of the remaining 4 employees in range S41-S60.

The salary of these 4 employess could be in the range $40,000 < S < $43,000 or $43,000 < S < $49,000 or $49,000 < S < $50,000.
Does it matter in which range it would be ? No, In all cases, the salary of S50 and S51 will be $43,000 each as there are 11 employees with a salary $43,000 a year

Median = (S50 + S51)/2 = ($43,000 + $43,000)/2 = $43,000.

Option A is the answer.

Hope it helps,
Clifin J Francis,
GMAT SME

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In a company 60% of the employees earn less than $50,000

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