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Lets say we are dealing with two items.
I think we all agree that using only the product or the sum we cannot find the individual prices.
But we can do that (in case of 2 items ) when we know both.......

Now with 4 items.... I think it can be done....... but the equation would be complex. Since I am not sure..... I will go with E.

Did you try solving for c and d to check if you get values that are in cents and not in fractions?

Obviously they can't be whole numbers. The only positive integers
that satisfy the first equations are 1-s. But that clearly contradicts the second one. However it doesn't mean that there is not enough info to get an answer as E states. The answer is that there is no answer. So it has to be C.

Did you try solving for c and d to check if you get values that are in cents and not in fractions?

Obviously they can't be whole numbers. The only positive integers that satisfy the first equations are 1-s. But that clearly contradicts the second one. However it doesn't mean that there is not enough info to get an answer as E states. The answer is that there is no answer. So it has to be C.

I would assume because you cannot have an answer, that's why choice E is there. C means when you can show valid answers from the information provided. Otherwise, for all questions, we can assume that answer is we cannot get a valid answer from the info provided and hence C. There is always an answer available, the question here is whether we have enough info to deduce them.
_________________

Did you try solving for c and d to check if you get values that are in cents and not in fractions?

Obviously they can't be whole numbers. The only positive integers that satisfy the first equations are 1-s. But that clearly contradicts the second one. However it doesn't mean that there is not enough info to get an answer as E states. The answer is that there is no answer. So it has to be C.

I would assume because you cannot have an answer, that's why choice E is there. C means when you can show valid answers from the information provided. Otherwise, for all questions, we can assume that answer is we cannot get a valid answer from the info provided and hence C. There is always an answer available, the question here is whether we have enough info to deduce them.

Nope, this is not correct. The DS question doesn't ask you what is the answer to the given question. The only thing the it asks is whether there is enough info to get ANY definite answer. The "no solution" answer is a definite answer. So this particular question provides just enough info to conclude that it doesn't have a solution so no additional information can change a thing. So that clearly cannot be E. That what I think.

Did you try solving for c and d to check if you get values that are in cents and not in fractions?

Obviously they can't be whole numbers. The only positive integers that satisfy the first equations are 1-s. But that clearly contradicts the second one. However it doesn't mean that there is not enough info to get an answer as E states. The answer is that there is no answer. So it has to be C.

I would assume because you cannot have an answer, that's why choice E is there. C means when you can show valid answers from the information provided. Otherwise, for all questions, we can assume that answer is we cannot get a valid answer from the info provided and hence C. There is always an answer available, the question here is whether we have enough info to deduce them.

Nope, this is not correct. The DS question doesn't ask you what is the answer to the given question. The only thing the it asks is whether there is enough info to get ANY definite answer. The "no solution" answer is a definite answer. So this particular question provides just enough info to conclude that it doesn't have a solution so no additional information can change a thing. So that clearly cannot be E. That what I think.

Yes you do have a valid point. I guess in this case Gmat (or gmatclub) is thinking that since we cannot identify 4 prices in cents or dollars, answer is E. This is probably not an original gmat question as Gmat tends to stay away from controversies.
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Yes you do have a valid point. I guess in this case Gmat (or gmatclub) is thinking that since we identify 4 prices in cents or dollars, answer is E. This is probably not an original gmat question as Gmat tends to stay away from controversies.

I'm sure it isn't. Just wanted to make sure I don't miss anything here.
Anyway thank you all for participation

Actually, I would say the answer is B, since we can determine that the price for the four items are 1,1,7 and 73 cents, respectively. However, this is a bad questions since (1) and (2) are not consistent. In real GMAT a rule of thumb is if there are solutions for (1) and (2), the solutions should be the same for both (although you are not required to actually provide the solutions). For example, it is not likely that you would get x=1 for (1) and x=3 for (2) and get D as an answer.
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Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.