gmat_guy666 wrote:An automated manufacturing unit employs N experts such that the range of their monthly salaries is $10,000. Their average monthly salary is $7000 above the lowest salary while the median monthly salary is only $5000 above the lowest salary. What is the minimum value of N?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 20
To make the math easier, use smaller numbers, as follows:
Range of the salaries = 10.
Lowest salary = 0.
Average salary = 7.
Median salary = 5.
Highest salary = 10.
We can PLUG IN THE ANSWERS, which represent the smallest possible number of employees.
Since we want the smallest possible value, start with the smallest answer choice.
Answer choice A: 10
Here, the sum of the 10 salaries = (number of employees)(average salary) = 10*7 = 70.
Since the median salary = 5, the sum of the 2 salaries in the middle = 10.
In ascending order, the 10 salaries could look as follows:
0, a, b, c, 5, 5, d, e, f, 10.
If a=b=c=5 and d=e=f=10, the greatest possible sum for the 10 salaries = 0 + (5*5) + (4*10) = 65.
Since the sum of the 7 salaries must by $70, eliminate A.
Answer choice B: 12
Here, the sum of the 12 salaries = (number of employees)(average salary) = 12*7 = 84.
Since the median salary = 5, the sum of the 2 salaries in the middle = 10.
In ascending order, the 12 salaries could look as follows:
0, a, b, c, d, 5, 5, e, f, g, h, 10.
If a=b=c=d=5 and e=f=g=h=10, the greatest possible sum for the 10 salaries = 0 + (6*5) + (5*10) = 80.
Since the sum of the 7 salaries must by $84, eliminate B.
Answer choice C: 14
Here, the sum of the 14 salaries = (number of employees)(average salary) = 14*7 = 98.
Since the median salary = 5, the sum of the 2 salaries in the middle = 10.
In ascending order, the 14 salaries could look as follows:
0, a, b, c, d, e, 5, 5, f, g, h, i, j, 10.
If a=b=c=d=e=5 and f=g=h=i=j=10, the greatest possible sum for the 14 salaries = 0 + (7*5) + (6*10) = 95.
Since the sum of the 7 salaries must by $98, eliminate C.
Answer choice D: 15
Here, the sum of the 15 salaries = (number of employees)(average salary) = 15*7 = 105.
In ascending order, the 15 salaries would look as follows:
0, a, b, c, d, e, f, 5, g, h, i, j, k, l, 10.
If a=b=c=d=e=f=5 and g=h=i=j=k=l=10, the greatest possible sum for the 15 salaries = 0 + (7*5) + (7*10) = 105.
Success!
The correct answer is
D.
