I've solved this with similar logic and didn't solve the equation. Although, I knew that this equation will come out to be a quadratic which might have both imaginary roots or 2 positive roots.
So, my question is about the assumption that Gmat will give a true scenario in statements which will for sure have one positive root only that will be an answer. Thus, we don't need to check if the equation has only 1 positive root.
Please, let me know if this assumption is wrong.
Bunuel wrote:
Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours. In how many hours can Rafael tabulate the data working alone?
(1) Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
(2) Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.
Information given:
Working together, Rafael and Salvador can tabulate a certain set of data in 2 hours.
Question:
In how many hours can Rafael tabulate the data working alone?
This question may seem complicated, but the truth is that since we know how long it takes for the two of them to complete the job, if we have any information that we can use to accurately compare how fast one works to how fast the other works, then we can answer the question.
Statement 1: Working alone, Rafael can tabulate the data in 3 hours less time than Salvador, working alone, can tabulate the data.
We do not need to use any math to determine whether this statement is sufficient. We have only to notice that we know how long it takes for both of them to do the work together and that we have information that we can use to determine their relative speeds. With that information, we could work our way to the answer to the question, how many hours Rafael would take to do the job alone.
To see why, consider this:
Time for Rafael to do the job = R
Time for Salvador to do the job = R + 3
We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time.
Sufficient.
Statement 2: Working alone, Rafael can tabulate the data in 1/2 the time that Salvador, working alone, can tabulate the data.
This tells us that Rafael works twice as fast as Salvador works. Since we know how long they take to do the job together, we can clearly work our way to Rafael's speed and then his time to do the job himself.
To see why, consider this:
Rafael's speed = 1/r
Salvador's speed = 1/2r
We are now working with one variable, and we have the time it takes for them to do the job together. So, we could work our way to Rafael's time, but we won't because this is a DS question.
Sufficient.
The correct answer is D.