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

Question

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

KarishmaB · Accepted Answer

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.

nvijayprasanna · Answer

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.

utkgogia2003 · Answer

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

gvij2017 · Answer

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.

Khusheesoni · Answer

if 66% earn more than 40k => 34% earn less than 40 k, which we will keep as the starting point
58% earning less than 50k is the end point
now 17% earning 45k implies that from 34th to 51st (34+17=51) percent people are earning 45k, or inversely, from 55th to 38th percent (58-3=55, 55-17=38) people are earning 45k

+17% +3% remaining
34%---------->51%-------->54%--------->58%
40k---------->45k-------->48k---------->50k

or

remaining -17% -3%
34%<-----------38%<---------55%<---------58%
40k<-----------45k<---------48k<---------50k

either way, 50th percent falls in the 45k bracket
hence median salary is 45k

Khusheesoni · Answer

if 66% earn more than 40k => 34% earn less than 40 k, which we will keep as the starting point
58% earning less than 50k is the end point
now 17% earning 45k implies that from 34th to 51st (34+17=51) percent people are earning 45k, or inversely, from 55th to 38th percent (58-3=55, 55-17=38) people are earning 45k

+17% +3% remaining
34%---------->51%-------->54%--------->58%
40k---------->45k-------->48k---------->50k

or

remaining -17% -3%
34%<-----------38%<---------55%<---------58%
40k<-----------45k<---------48k<---------50k

either way, 50th percent falls in the 45k bracket
hence median salary is 45k

bumpbot · Answer

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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%

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