The owner of an art shop conducts his business in the follow

Let's start with something very important... you will NEVER see questions with numbers as complicated as these on the actual GMAT. So, while this question discusses concepts that are certainly testable, the numbers involved are not. The only way to solve this is by doing very complicated calculations, something you'll never have to do on test day.

Now that we've gotten that out of the way, let's talk about how we could solve efficiently: backsolving.

First, let's arrange the answers from smallest to biggest (on the actual GMAT it's very rare for the numbers to be out of order, so you very rarely need to rearrange):

D) 2000
B) 2256.25
C) 2500
A) 2756.25
E) 5000

If this were the actual GMAT, I'd immediately eliminate B and A, since there's no way numbers that bizarre would ever be correct. On this question that would have been a bad decision, another indication of how unGMATesque this question really is.

Nonetheless, I'd now have:

D) 2000
C) 2500
E) 5000

I'd then use common sense: if my first deduction was $411, then the answer has to be more than $1944 + 411. Accordingly, I'd eliminate D)2000 as well.

Now we could just plug in one of the two remaining choices. Let's say we decide to work with $2500.

We know after the first round the price decreased by $411. So:

original price - (OP)(1+x)(1-x) = 411

2500 - (2500)(1 - x^2) = 411

2500 - 2500 + 2500x^2 = 411

2500x^2 = 411

x^2 = 411/2500

we would use this to solve for x.

Again, on the actual GMAT (does this sound repetitive yet?), the numbers would all work out nicely for the correct answer. Assuming that everything worked out and I got a nice simple value for x, we'd move on to step 2, applying the second cycle:

2500-411 = 2089

2089(1 + x)(1 - x) [we know the value for x now, so we'd just do the math]

If our final value is $1944.81, then $2500 is correct. If our final value is less than $1944.81, then the other answer must be correct.

* * *

Now, we could have used strategic eliminate on the question as presented to determine that (A) is in fact the only possible answer.

We know that our first reduction is $411. As our number gets smaller, the amount of the reduction each cycle will also decrease. So, we can set up:

Original amount - $411 - something smaller than $411 = $1944.81

$2000 and $2256 are both clearly too small: eliminate (B) and (D); $5000 is clearly too big, eliminate (E).

2500 - 411 is 2089. Do we think the second reduction is only going to be $145? No, that's way too small compared to $411: eliminate (C).

Only (A) remains, all done.

* * *

Just in case I haven't said it enough times: there is no way you'd ever see a GMAT question with these numbers in it. What's the source?