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.
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >