Each statement is sufficient. The answer is D

Basically the average for the entire cycle depends on when the employee was hired. if there had been no hiring, the average would have been the fixed $5,750. On the other hand, if the new employee had been there for the entire month, the average would have been the fixed $5,750+280=$6,030. The exact average is somewhere between these two values. If the employee was hired very early (such as day 1 or day 2), then the average would be very close to $6030. On the other hand, if the employee was hired very late (such as the last day) then his salary would have a minimal impact and the average would be very close to $5,750.

Rephrase: When was the employee hired?

(1) Directly answers the rephrase. SUFFICIENT

(2) By day 20, since the average is no longer 5750, we know that the new employee has been hired. Since we know that the average at day 20 is about half way between 5750 and 6030, we can determine when the employee was hired (halfway between the start of the period and day 20). Thus this answers our rephrase (notice that this info is consistent with statement 1). SUFFICIENT

If you're not convinced, consider the algebra: Of the first 20 days, There were n days during which the average was $5,750. Then there were 20-n days during which the average was $6,030. Over the whole 20 days, the average was $5,890. This allows us to write the weighted average formula: [5750*n + 6030*(20-n)]/20 = 5890. From this we can find n, the number of days before the employee was hired. This directly answers our rephrase. SUFFICIENT
[spoiler]
The answer is D[/spoiler]. This question was made using GMATPrep Question 1484 as a template. To practice similar questions, create a drill by setting topic='Translations & Manipulations' and difficulty='700+' in the Drill Generator

-Patrick