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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Karishma

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