Can you guide me to the explanation to the math review guide? I am not able to understand the answers to some of the questions like this
Assume there are n employees in Department Y, then Department X has more than 2n employees.
The average salary in Department X is 25,000
The average salary in Department Y is 35,000
Sum = Avg x Count
Sum of salaries in Department X = 25,000 * 2n
Sum of salaries in Department Y = 35,000 * n
Sum of salaries in the entire company = 25,000 * 2n + 35,000 * n
Average (entire company) = \frac{25,000 * 2n + 35,000 * n}{2n + n}
Now you can choose a number for n, say n = 10, which will make calculations simpler.
If we take n = 10, then the
Average = \frac{25,000 * 2 * 10 + 35,000 * 10}{2 * 10 + 10}
Average = \frac{850000}{30}
Average = 28,333
In the above calculations, we used the number of employees in department X as 2n. Notice that the question states more than 2n. For all we know, it could be in the millions. There is no upper bound defined. Only the lower bound is given (2n), which is what we used. The average we got 28,333 is the highest average possible. So the answer is A and B.
This might be intuitive to some. But to explain it, Imagine there are 10 employees in Department Y and 100 employees in Department X
the average salary of the company = 25,909
Now imagine there are 10 employees in Department Y and 1000 employees in Department X
the average salary of the company = 25,099
So as the number of employees in Department X increases (remember the question doesn’t specify an upper bound), the average goes down since they get significantly lesser pay than Department B.
Thank you! This made things a lot clearer!
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