word 'initially' in the question bothers me.
can we assume that in B he sold the product at a 40% markup? If that's the case, the answer is D.
If not, then it's A.
I put A b/c we don't know what the final mark-up % is in a case of B.
Good job, lastochka!
I think this is a great problem to help understand Data Sufficiency. Read this whole thing (I know it's long). There's a lesson down towards the bottom somewhere.
The word "initially" is key here. If he sold it for $1953, how do we know it's still 40% discount?
The first one definately does work:
If C is the original cost, then the original asking price would have been 1.4C (40% more than C). But since he reduced that by 10%, we can say .9(1.4C) is the amount he did sell it for. That, minus his cost, = 403:
.9(1.4C) - C = 403.
So with one variable we can solve the problem.
Now, on to number 2.
Let's say you ignored the word "initially". Taken in a vacuum, number 2 should be enough too. Of course if we know what he sold it for, we should be able to write: 1.4C=1953.
And since we've already dismissed number 1 as correct, and since we're following the classic "If A then A or D" approach to data sufficiency, we block out number 1 and say that number 2 is enough, too, so it's got to be D.
In number one, HE DID REDUCE THE PRICE BY 10% MORE! Where is that information in number 2? Can we possibly know that?
Remember, and this is the major point of this question: The data sufficiency statements will NEVER contradict themselves. If he reduced it by 10% in the first one, he MUST have reduced it by 10% in the second one. But there's no mention of it. So we should be forced to say, "huh! Is this a further reduced price?" Which would make you read the question again and see the word "initially," which should make you think, "Nope, there's no way to know what the story is with this one."
So the answer has to be A.
Want proof? Do the math in the first two:
1) .9(1.4C) - C = 403
C = 1550
If that was his cost, and he made $403, then he sold it for $1953, exactly the number that's written in number 2.
If we did the math in number 2 without taking the "initially" into account, the cost would have been $1395, and the profit would have been $558. That doesn't match with number 1, so somewhere he must have changed the price.
So. What do we learn? We've been able to use information from Statement 1 to help us decide what to do with Statement 2. That doesn't mean we're going to choose C. It can't be that, because the answer's A. But please remember that in the GMAT, every piece of every question is information, and that's information you can use to figure out what to do with different parts of the problem. Use the statments against themselves!
They won't contradict each other. If you know that, you've gained some real power over the GMAT.
By the way, this is a real question, word for word, published in some old book I've got.