Data Sufficiency

An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?

(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%

OA is E

Why it cannot be C

My answer is C. Here is the reason:

For statement 1: 20 cars were sold for $20,000
->this implies that the other 30 cars were sold for $30,000 since "An auto dealer sells each car at either $20,000 or $30,000". But we don't have any information about the mark up, so this statement is insufficient
For statement 2: 30 cars were marked up 30%
->this implies that the other 20 cars were marked up 20% since "Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price". But we don't have any information about the price of these 30 cars, so this statement is insufficient
Combine statement 1 and 2, we have the total price and mark up for all the cars, so C is correct.

Each car is sold at either 20,000 or 30,000 dollars
Total cars sold = 50
What is the total profit of the dealer?
Total profit =Total selling price - Total cost price

Statement 1
20 cars were sold for 20,000 dollars , hence 30 cars (remaining) were sold for 30,000 dollars
Total profit = Total selling price - Total cost price
Profit for 20 cars = Selling price for 20 cars - cost price for 20 cars
$$=20-x$$
cost price for cars is unknown, hence statement is INSUFFICIENT

Statement 2
30 cars were marked up by 30% hence remaining 20 cars will be marked up by 20%
Profit for 30 cars = Selling price for 30 cars - Cost price for 30 cars
(30% of the price + Cost price) = Profit for 30 cars
Cost price for all cars is unknown hence statement 2 is INSUFFICIENT

combining statement 1 and 2 together
20 cars were sold for 20,000 dollars
30 cars were sold for 30,000 dollars
20 cars were marked up by 20%
30 cars were marked up by 30%
$$Let\ the\ price\ of\ 20\ cars\ =x$$
selling of 20 cars =20,000 dollars
$$\Pr ofit=20\%\ of\ x$$ $$\Pr ofit=20\%\ of\ x$$ $$\frac{20}{100}\cdot x=20,000-x$$ $$0.2x=20,000-x$$
$$\frac{1.2x}{1.2}=\frac{20000}{1.2}$$
$$x=16,666.7 dollars$$
cost price of 20 cars =16,666.7 dollars
Let cost price of 30 cars = y
selling price of 30 cars =30,000 dollars
Profit = 30% of y
Profit = Selling Price - Cost price
$$\frac{30}{100}\cdot y=30000-y$$
$$0.3y=3000-y$$
$$\frac{1.3y}{1.3}=\frac{30000}{1.3}$$
$$y=23,076.9 dollars$$
$$20\%\ of\ \ x=\frac{20}{100}\cdot16666.7$$
$$=0.2\cdot16666.7$$
$$=3333.34$$ $$30\%\ of\ \ y=\frac{30}{100}\cdot23,076.9$$
$$=0.3\cdot23,076.9$$
$$=6923.07 dollars$$
$$Total\ profit=3333.34+6923.07$$
$$=10,256.41\ dollars$$
$$hence\ Statement\ 1\ and\ \ 2\ together\ are\ SUFFICIENT$$
$$answer=option\ C$$

I also believe that answer is C, but e-gmat's says OA is E. Here's the link https://gmatclub.com/forum/an-auto-deal ... 28882.html

What are your thoughts ? I am still confused.