Data Sufficiency

An automated manufacturing unit employs N experts. Their average monthly salary is $7000 while the
median monthly salary is only $5000. If the range (difference between highest and lowest) of their monthly
salaries is $10,000, is the salary of highest paid expert more than $12,000?
I. N <5
II. N = 8

$$average\ monthly\ salary=7,000\ dollars$$
$$median\ monthly\ salary=5,000\ dollars$$
range = Highest - Lowest salary = 10,000 dollars
Is the salary of the highest paid expert more than 12,000 dollars ?

Statement 1
N<5, this means number of experts can be either 1, 2, 3, or 4.
If experts = 4, Let highest paid expert salary = H
Range = Highest - Lowest
$$lowest\ Salary=H-\ 10,000\ dollars\ $$
$$Average\ monthly\ salary=\frac{\left(\left(H-10,000\right)+5,000+5,000+H\right)}{4}$$ $$7,000=\frac{\left(H-10,000+10,000+H\right)}{4}$$ $$28,000=\left(2H\right)$$ $$H=14,000\ dollars\ $$ $$H>12,000\ dollars\ $$
If experts = 2
$$Average=\ \frac{\left(5,000\ +5,000\ \right)}{2}dollars\ $$
Highest paid worker salary is < 12,000 dollars .This is false, hence
$$statement\ 1\ is\ INSUFFICIENT.$$

Statement 2
N = 8
$$Average\ Monthly\ Salary=\frac{SUM}{N}$$ $$7,000=\frac{SUM}{8},\ SUM\ =56,000$$
if N = 3 and highest paid worker = H
$$Average=\frac{\left(H-10,000+5,000+H\right)}{3}$$
$$7,000\cdot3=2H-5,000$$
$$\left(21000+5000\right)dollars=2H$$
$$H=\frac{\left(26,000\right)}{2}=13,000\ dollars\ $$
For H to be greater than 12,000 dollars, N has to be greater than or equal to 3, hence
$$statement\ 2\ is\ INSUFFICIENT.$$

$$answer\ is\ Option\ B$$