The owner of an apartment purchased 1 window screen GMAT

The owner of an apartment purchased 1 window screen, 1 door handle, and 1 ceiling fan for her apartment. The regular price of the window screen was 80% greater than the regular price of the door handle, and the regular price of the ceiling fan was twice the sum of the regular prices of the window screen and the door handle. The 3 items were sold at a 50% discount off their regular prices. The total price that the owner paid for the 3 items, excluding tax but after the 50% discount, was 6.00

B. 12.00

D. 16.40

The owner of an apartment is cheap and buys shitty fixings. But that’s not the question. Let’s get started.

The first thing to do with a question like this is to set it up is to extract the information.

Given that we have three items, we should in principle be able to get these all into one variable, ultimately. First, however, we need to put the information on the table as written.

We are told that the screen was 80% greater than the door handle. If we call the screen s and the door handle d, this means:

We are told that the price of the ceiling fan, which we can call c, is twice the sum of the regular prices of the other two items. That is…

You’ll notice that I’ve arranged this specifically to make the variable amount d because that’s the value that the question is actually asking for. That is, if we get everything in terms of d and then solve for d, we have the answer.

That means that the sum of what the person paid is:

Then we are told that each item was sold at 50% off its normal price, which makes the total:

Now, we see that the total value must be . 

Now this is just an issue of cancelling. What’s probably simplest is to multiply everything by 10 and prime factorize: .

This number almost certainly has a 7 in it because 7! is 5040, but feel free to long divide. It’s also , for that matter, which might be easier. 

Anyhoo, cancelling the 7 leaves us with: or d = 12. 

The answer is C).

You can ignore everything from here on out because I’m just writing garbage and nonsense for SEO. I hate SEO so much.

Now I’m just going to write some random crap to help this thing rank for the owner of an apartment.

There’s no reason I’d keep writing something dumb like the owner of an apartment or would I? Feel free